diff --git a/deepmd/descriptor/__init__.py b/deepmd/descriptor/__init__.py
index 3e2c0e59b0..4a8356b46a 100644
--- a/deepmd/descriptor/__init__.py
+++ b/deepmd/descriptor/__init__.py
@@ -17,6 +17,9 @@
     DescrptSeAEf,
     DescrptSeAEfLower,
 )
+from .se_a_mask import (
+    DescrptSeAMask,
+)
 from .se_atten import (
     DescrptSeAtten,
 )
diff --git a/deepmd/descriptor/se_a_mask.py b/deepmd/descriptor/se_a_mask.py
new file mode 100644
index 0000000000..6e5d686c19
--- /dev/null
+++ b/deepmd/descriptor/se_a_mask.py
@@ -0,0 +1,433 @@
+import math
+import warnings
+from typing import (
+    Any,
+    Dict,
+    List,
+    Optional,
+    Tuple,
+)
+
+import numpy as np
+
+from deepmd.common import (
+    get_activation_func,
+    get_precision,
+)
+from deepmd.env import (
+    GLOBAL_NP_FLOAT_PRECISION,
+    GLOBAL_TF_FLOAT_PRECISION,
+    default_tf_session_config,
+    op_module,
+    tf,
+)
+from deepmd.utils.argcheck import (
+    list_to_doc,
+)
+from deepmd.utils.graph import (
+    get_tensor_by_name_from_graph,
+    load_graph_def,
+)
+from deepmd.utils.network import (
+    embedding_net,
+    embedding_net_rand_seed_shift,
+)
+from deepmd.utils.sess import (
+    run_sess,
+)
+from deepmd.utils.tabulate import (
+    DPTabulate,
+)
+from deepmd.utils.type_embed import (
+    embed_atom_type,
+)
+
+from .descriptor import (
+    Descriptor,
+)
+from .se_a import (
+    DescrptSeA,
+)
+
+
+@Descriptor.register("se_a_mask")
+class DescrptSeAMask(DescrptSeA):
+    r"""DeepPot-SE constructed from all information (both angular and radial) of
+    atomic configurations. The embedding takes the distance between atoms as input.
+
+    The descriptor :math:`\mathcal{D}^i \in \mathcal{R}^{M_1 \times M_2}` is given by [1]_
+
+    .. math::
+        \mathcal{D}^i = (\mathcal{G}^i)^T \mathcal{R}^i (\mathcal{R}^i)^T \mathcal{G}^i_<
+
+    where :math:`\mathcal{R}^i \in \mathbb{R}^{N \times 4}` is the coordinate
+    matrix, and each row of :math:`\mathcal{R}^i` can be constructed as follows
+
+    .. math::
+        (\mathcal{R}^i)_j = [
+        \begin{array}{c}
+            s(r_{ji}) & \frac{s(r_{ji})x_{ji}}{r_{ji}} & \frac{s(r_{ji})y_{ji}}{r_{ji}} & \frac{s(r_{ji})z_{ji}}{r_{ji}}
+        \end{array}
+        ]
+
+    where :math:`\mathbf{R}_{ji}=\mathbf{R}_j-\mathbf{R}_i = (x_{ji}, y_{ji}, z_{ji})` is
+    the relative coordinate and :math:`r_{ji}=\lVert \mathbf{R}_{ji} \lVert` is its norm.
+    The switching function :math:`s(r)` is defined as:
+
+    .. math::
+        s(r)=
+        \begin{cases}
+        \frac{1}{r}, & r<r_s \\
+        \frac{1}{r} \{ {(\frac{r - r_s}{ r_c - r_s})}^3 (-6 {(\frac{r - r_s}{ r_c - r_s})}^2 +15 \frac{r - r_s}{ r_c - r_s} -10) +1 \}, & r_s \leq r<r_c \\
+        0, & r \geq r_c
+        \end{cases}
+
+    Each row of the embedding matrix  :math:`\mathcal{G}^i \in \mathbb{R}^{N \times M_1}` consists of outputs
+    of a embedding network :math:`\mathcal{N}` of :math:`s(r_{ji})`:
+
+    .. math::
+        (\mathcal{G}^i)_j = \mathcal{N}(s(r_{ji}))
+
+    :math:`\mathcal{G}^i_< \in \mathbb{R}^{N \times M_2}` takes first :math:`M_2`$` columns of
+    :math:`\mathcal{G}^i`$`. The equation of embedding network :math:`\mathcal{N}` can be found at
+    :meth:`deepmd.utils.network.embedding_net`.
+    Specially for descriptor se_a_mask is a concise implementation of se_a.
+    The difference is that se_a_mask only considered a non-pbc system.
+    And accept a mask matrix to indicate the atom i in frame j is a real atom or not.
+    (1 means real atom, 0 means ghost atom)
+    Thus se_a_mask can accept a variable number of atoms in a frame.
+
+    Parameters
+    ----------
+    sel : list[str]
+            sel[i] specifies the maxmum number of type i atoms in the neighbor list.
+    neuron : list[int]
+            Number of neurons in each hidden layers of the embedding net :math:`\mathcal{N}`
+    axis_neuron
+            Number of the axis neuron :math:`M_2` (number of columns of the sub-matrix of the embedding matrix)
+    resnet_dt
+            Time-step `dt` in the resnet construction:
+            y = x + dt * \phi (Wx + b)
+    trainable
+            If the weights of embedding net are trainable.
+    seed
+            Random seed for initializing the network parameters.
+    type_one_side
+            Try to build N_types embedding nets. Otherwise, building N_types^2 embedding nets
+    exclude_types : List[List[int]]
+            The excluded pairs of types which have no interaction with each other.
+            For example, `[[0, 1]]` means no interaction between type 0 and type 1.
+    activation_function
+            The activation function in the embedding net. Supported options are {0}
+    precision
+            The precision of the embedding net parameters. Supported options are {1}
+    uniform_seed
+            Only for the purpose of backward compatibility, retrieves the old behavior of using the random seed
+    References
+    ----------
+    .. [1] Linfeng Zhang, Jiequn Han, Han Wang, Wissam A. Saidi, Roberto Car, and E. Weinan. 2018.
+       End-to-end symmetry preserving inter-atomic potential energy model for finite and extended
+       systems. In Proceedings of the 32nd International Conference on Neural Information Processing
+       Systems (NIPS'18). Curran Associates Inc., Red Hook, NY, USA, 4441–4451.
+    """
+
+    def __init__(
+        self,
+        sel: List[str],
+        neuron: List[int] = [24, 48, 96],
+        axis_neuron: int = 8,
+        resnet_dt: bool = False,
+        trainable: bool = True,
+        type_one_side: bool = False,
+        exclude_types: List[List[int]] = [],
+        seed: int = None,
+        activation_function: str = "tanh",
+        precision: str = "default",
+        uniform_seed: bool = False,
+    ) -> None:
+        """
+        Constructor
+        """
+        self.sel_a = sel
+        self.total_atom_num = np.cumsum(self.sel_a)[-1]
+        self.ntypes = len(self.sel_a)
+        self.filter_neuron = neuron
+        self.n_axis_neuron = axis_neuron
+        self.filter_resnet_dt = resnet_dt
+        self.seed = seed
+        self.uniform_seed = uniform_seed
+        self.seed_shift = embedding_net_rand_seed_shift(self.filter_neuron)
+        self.trainable = trainable
+        self.compress_activation_fn = get_activation_func(activation_function)
+        self.filter_activation_fn = get_activation_func(activation_function)
+        self.filter_precision = get_precision(precision)
+        self.exclude_types = set()
+        for tt in exclude_types:
+            assert len(tt) == 2
+            self.exclude_types.add((tt[0], tt[1]))
+            self.exclude_types.add((tt[1], tt[0]))
+        self.set_davg_zero = False
+        self.type_one_side = type_one_side
+        # descrpt config. Not used in se_a_mask
+        self.sel_r = [0 for ii in range(len(self.sel_a))]
+        self.ntypes = len(self.sel_a)
+        assert self.ntypes == len(self.sel_r)
+        self.rcut_a = -1
+        # numb of neighbors and numb of descrptors
+        self.nnei_a = np.cumsum(self.sel_a)[-1]
+        self.nnei = self.nnei_a
+
+        self.ndescrpt_a = self.nnei_a * 4
+        self.ndescrpt = self.ndescrpt_a
+        self.useBN = False
+        self.dstd = None
+        self.davg = None
+        self.rcut = -1.0  # Not used in se_a_mask
+        self.compress = False
+        self.embedding_net_variables = None
+        self.mixed_prec = None
+        self.place_holders = {}
+        nei_type = np.array([])
+        for ii in range(self.ntypes):
+            nei_type = np.append(nei_type, ii * np.ones(self.sel_a[ii]))  # like a mask
+        self.nei_type = tf.constant(nei_type, dtype=tf.int32)
+
+        avg_zero = np.zeros([self.ntypes, self.ndescrpt]).astype(
+            GLOBAL_NP_FLOAT_PRECISION
+        )
+        std_ones = np.ones([self.ntypes, self.ndescrpt]).astype(
+            GLOBAL_NP_FLOAT_PRECISION
+        )
+        sub_graph = tf.Graph()
+        with sub_graph.as_default():
+            name_pfx = "d_sea_mask_"
+            for ii in ["coord", "box"]:
+                self.place_holders[ii] = tf.placeholder(
+                    GLOBAL_NP_FLOAT_PRECISION, [None, None], name=name_pfx + "t_" + ii
+                )
+            self.place_holders["type"] = tf.placeholder(
+                tf.int32, [None, None], name=name_pfx + "t_type"
+            )
+            self.place_holders["mask"] = tf.placeholder(
+                tf.int32, [None, None], name=name_pfx + "t_aparam"
+            )  # named aparam for inference compatibility in c++ interface.
+
+            self.place_holders["natoms_vec"] = tf.placeholder(
+                tf.int32, [self.ntypes + 2], name=name_pfx + "t_natoms"
+            )  # Not used in se_a_mask. For compatibility with c++ interface.
+            self.place_holders["default_mesh"] = tf.placeholder(
+                tf.int32, [None], name=name_pfx + "t_mesh"
+            )  # Not used in se_a_mask. For compatibility with c++ interface.
+
+            self.stat_descrpt, descrpt_deriv, rij, nlist = op_module.descrpt_se_a_mask(
+                self.place_holders["coord"],
+                self.place_holders["type"],
+                self.place_holders["mask"],
+                self.place_holders["box"],
+                self.place_holders["natoms_vec"],
+                self.place_holders["default_mesh"],
+            )
+        self.sub_sess = tf.Session(graph=sub_graph, config=default_tf_session_config)
+        self.original_sel = None
+
+    def get_rcut(self) -> float:
+        """
+        Returns: the cutoff radius:
+        """
+        warnings.warn("The cutoff radius is not used for this descriptor")
+        return -1.0
+
+    def compute_input_stats(
+        self,
+        data_coord: list,
+        data_box: list,
+        data_atype: list,
+        natoms_vec: list,
+        mesh: list,
+        input_dict: dict,
+    ) -> None:
+        """
+        Compute the statisitcs (avg and std) of the training data. The input will be normalized by the statistics.
+
+        Parameters
+        ----------
+        data_coord
+            The coordinates. Can be generated by deepmd.model.make_stat_input
+        data_box
+            The box. Can be generated by deepmd.model.make_stat_input
+        data_atype
+            The atom types. Can be generated by deepmd.model.make_stat_input
+        natoms_vec
+            The vector for the number of atoms of the system and different types of atoms. Can be generated by deepmd.model.make_stat_input
+        mesh
+            The mesh for neighbor searching. Can be generated by deepmd.model.make_stat_input
+        input_dict
+            Dictionary for additional input
+        """
+
+        """
+        TODO: Since not all input atoms are real in se_a_mask,
+        statistics should be reimplemented for se_a_mask descriptor.
+        """
+
+        self.davg = None
+        self.dstd = None
+
+    def build(
+        self,
+        coord_: tf.Tensor,
+        atype_: tf.Tensor,
+        natoms: tf.Tensor,
+        box_: tf.Tensor,
+        mesh: tf.Tensor,
+        input_dict: Dict[str, Any],
+        reuse: Optional[bool] = None,
+        suffix: str = "",
+    ) -> tf.Tensor:
+        """
+        Build the computational graph for the descriptor
+
+        Parameters
+        ----------
+        coord_
+            The coordinate of atoms
+        atype_
+            The type of atoms
+        natoms
+            The number of atoms. This tensor has the length of Ntypes + 2
+            natoms[0]: number of local atoms
+            natoms[1]: total number of atoms held by this processor
+            natoms[i]: 2 <= i < Ntypes+2, number of type i atoms
+        mesh
+            For historical reasons, only the length of the Tensor matters.
+            if size of mesh == 6, pbc is assumed.
+            if size of mesh == 0, no-pbc is assumed.
+        input_dict
+            Dictionary for additional inputs
+        reuse
+            The weights in the networks should be reused when get the variable.
+        suffix
+            Name suffix to identify this descriptor
+
+        Returns
+        -------
+        descriptor
+            The output descriptor
+        """
+        davg = self.davg
+        dstd = self.dstd
+
+        """
+        ``aparam'' shape is [nframes, natoms]
+        aparam[:, :] is the real/virtual sign for each atom.
+        """
+        aparam = input_dict["aparam"]
+        self.mask = tf.cast(aparam, tf.int32)
+        self.mask = tf.reshape(self.mask, [-1, natoms[1]])
+
+        with tf.variable_scope("descrpt_attr" + suffix, reuse=reuse):
+            if davg is None:
+                davg = np.zeros([self.ntypes, self.ndescrpt])
+            if dstd is None:
+                dstd = np.ones([self.ntypes, self.ndescrpt])
+            t_rcut = tf.constant(
+                self.rcut,
+                name="rcut",
+                dtype=GLOBAL_TF_FLOAT_PRECISION,
+            )
+            t_ntypes = tf.constant(self.ntypes, name="ntypes", dtype=tf.int32)
+            t_ndescrpt = tf.constant(self.ndescrpt, name="ndescrpt", dtype=tf.int32)
+            t_sel = tf.constant(self.sel_a, name="sel", dtype=tf.int32)
+            """
+            self.t_avg = tf.get_variable('t_avg',
+                                         davg.shape,
+                                         dtype = GLOBAL_TF_FLOAT_PRECISION,
+                                         trainable = False,
+                                         initializer = tf.constant_initializer(davg))
+            self.t_std = tf.get_variable('t_std',
+                                         dstd.shape,
+                                         dtype = GLOBAL_TF_FLOAT_PRECISION,
+                                         trainable = False,
+                                         initializer = tf.constant_initializer(dstd))
+            """
+
+        coord = tf.reshape(coord_, [-1, natoms[1] * 3])
+        box_ = tf.reshape(
+            box_, [-1, 9]
+        )  # Not used in se_a_mask descriptor. For compatibility in c++ inference.
+        atype = tf.reshape(atype_, [-1, natoms[1]])
+
+        (
+            self.descrpt,
+            self.descrpt_deriv,
+            self.rij,
+            self.nlist,
+        ) = op_module.descrpt_se_a_mask(coord, atype, self.mask, box_, natoms, mesh)
+        # only used when tensorboard was set as true
+        tf.summary.histogram("descrpt", self.descrpt)
+        tf.summary.histogram("rij", self.rij)
+        tf.summary.histogram("nlist", self.nlist)
+
+        self.descrpt_reshape = tf.reshape(self.descrpt, [-1, self.ndescrpt])
+        self._identity_tensors(suffix=suffix)
+
+        self.dout, self.qmat = self._pass_filter(
+            self.descrpt_reshape,
+            atype,
+            natoms,
+            input_dict,
+            suffix=suffix,
+            reuse=reuse,
+            trainable=self.trainable,
+        )
+
+        # only used when tensorboard was set as true
+        tf.summary.histogram("embedding_net_output", self.dout)
+        return self.dout
+
+    def prod_force_virial(
+        self,
+        atom_ener: tf.Tensor,
+        natoms: tf.Tensor,
+    ) -> Tuple[tf.Tensor, tf.Tensor, tf.Tensor]:
+        """
+        Compute force and virial
+
+        Parameters
+        ----------
+        atom_ener
+            The atomic energy
+        natoms
+            The number of atoms. This tensor has the length of Ntypes + 2
+            natoms[0]: number of local atoms
+            natoms[1]: total number of atoms held by this processor
+            natoms[i]: 2 <= i < Ntypes+2, number of type i atoms
+
+        Returns
+        -------
+        force
+            The force on atoms
+        virial
+            None for se_a_mask op
+        atom_virial
+            None for se_a_mask op
+        """
+        [net_deriv] = tf.gradients(atom_ener, self.descrpt_reshape)
+        tf.summary.histogram("net_derivative", net_deriv)
+        net_deriv_reshape = tf.reshape(net_deriv, [-1, natoms[0] * self.ndescrpt])
+        force = op_module.prod_force_se_a_mask(
+            net_deriv_reshape,
+            self.descrpt_deriv,
+            self.mask,
+            self.nlist,
+            total_atom_num=self.total_atom_num,
+        )
+
+        tf.summary.histogram("force", force)
+
+        # Construct virial and atom virial tensors to avoid reshape errors in model/ener.py
+        # They are not used in se_a_mask op
+        virial = tf.zeros([1, 9], dtype=force.dtype)
+        atom_virial = tf.zeros([1, natoms[1], 9], dtype=force.dtype)
+
+        return force, virial, atom_virial
diff --git a/deepmd/fit/ener.py b/deepmd/fit/ener.py
index c4ece01fa7..4866186bfc 100644
--- a/deepmd/fit/ener.py
+++ b/deepmd/fit/ener.py
@@ -120,6 +120,9 @@ class EnerFitting(Fitting):
     layer_name : list[Optional[str]], optional
             The name of the each layer. If two layers, either in the same fitting or different fittings,
             have the same name, they will share the same neural network parameters.
+    use_aparam_as_mask: bool, optional
+            If True, the atomic parameters will be used as a mask that determines the atom is real/virtual.
+            And the aparam will not be used as the atomic parameters for embedding.
     """
 
     def __init__(
@@ -138,6 +141,7 @@ def __init__(
         precision: str = "default",
         uniform_seed: bool = False,
         layer_name: Optional[List[Optional[str]]] = None,
+        use_aparam_as_mask: bool = False,
     ) -> None:
         """
         Constructor
@@ -145,6 +149,7 @@ def __init__(
         # model param
         self.ntypes = descrpt.get_ntypes()
         self.dim_descrpt = descrpt.get_dim_out()
+        self.use_aparam_as_mask = use_aparam_as_mask
         # args = ()\
         #        .add('numb_fparam',      int,    default = 0)\
         #        .add('numb_aparam',      int,    default = 0)\
@@ -549,16 +554,18 @@ def build(
             assert len(bias_atom_e) == self.ntypes
 
         fparam = None
-        aparam = None
         if self.numb_fparam > 0:
             fparam = input_dict["fparam"]
             fparam = tf.reshape(fparam, [-1, self.numb_fparam])
             fparam = (fparam - t_fparam_avg) * t_fparam_istd
-        if self.numb_aparam > 0:
-            aparam = input_dict["aparam"]
-            aparam = tf.reshape(aparam, [-1, self.numb_aparam])
-            aparam = (aparam - t_aparam_avg) * t_aparam_istd
-            aparam = tf.reshape(aparam, [-1, self.numb_aparam * natoms[0]])
+
+        aparam = None
+        if not self.use_aparam_as_mask:
+            if self.numb_aparam > 0:
+                aparam = input_dict["aparam"]
+                aparam = tf.reshape(aparam, [-1, self.numb_aparam])
+                aparam = (aparam - t_aparam_avg) * t_aparam_istd
+                aparam = tf.reshape(aparam, [-1, self.numb_aparam * natoms[0]])
 
         atype_nall = tf.reshape(atype, [-1, natoms[1]])
         self.atype_nloc = tf.reshape(
diff --git a/deepmd/loss/ener.py b/deepmd/loss/ener.py
index 7c8d997c6a..900619c093 100644
--- a/deepmd/loss/ener.py
+++ b/deepmd/loss/ener.py
@@ -107,38 +107,48 @@ def build(self, learning_rate, natoms, model_dict, label_dict, suffix):
             atom_ener_coeff = label_dict["atom_ener_coeff"]
             atom_ener_coeff = tf.reshape(atom_ener_coeff, tf.shape(atom_ener))
             energy = tf.reduce_sum(atom_ener_coeff * atom_ener, 1)
-        l2_ener_loss = tf.reduce_mean(
-            tf.square(energy - energy_hat), name="l2_" + suffix
-        )
+        if self.has_e:
+            l2_ener_loss = tf.reduce_mean(
+                tf.square(energy - energy_hat), name="l2_" + suffix
+            )
+
+        if self.has_f or self.has_pf or self.relative_f:
+            force_reshape = tf.reshape(force, [-1])
+            force_hat_reshape = tf.reshape(force_hat, [-1])
+            diff_f = force_hat_reshape - force_reshape
 
-        force_reshape = tf.reshape(force, [-1])
-        force_hat_reshape = tf.reshape(force_hat, [-1])
-        atom_pref_reshape = tf.reshape(atom_pref, [-1])
-        diff_f = force_hat_reshape - force_reshape
         if self.relative_f is not None:
             force_hat_3 = tf.reshape(force_hat, [-1, 3])
             norm_f = tf.reshape(tf.norm(force_hat_3, axis=1), [-1, 1]) + self.relative_f
             diff_f_3 = tf.reshape(diff_f, [-1, 3])
             diff_f_3 = diff_f_3 / norm_f
             diff_f = tf.reshape(diff_f_3, [-1])
-        l2_force_loss = tf.reduce_mean(tf.square(diff_f), name="l2_force_" + suffix)
-        l2_pref_force_loss = tf.reduce_mean(
-            tf.multiply(tf.square(diff_f), atom_pref_reshape),
-            name="l2_pref_force_" + suffix,
-        )
 
-        virial_reshape = tf.reshape(virial, [-1])
-        virial_hat_reshape = tf.reshape(virial_hat, [-1])
-        l2_virial_loss = tf.reduce_mean(
-            tf.square(virial_hat_reshape - virial_reshape), name="l2_virial_" + suffix
-        )
+        if self.has_f:
+            l2_force_loss = tf.reduce_mean(tf.square(diff_f), name="l2_force_" + suffix)
 
-        atom_ener_reshape = tf.reshape(atom_ener, [-1])
-        atom_ener_hat_reshape = tf.reshape(atom_ener_hat, [-1])
-        l2_atom_ener_loss = tf.reduce_mean(
-            tf.square(atom_ener_hat_reshape - atom_ener_reshape),
-            name="l2_atom_ener_" + suffix,
-        )
+        if self.has_pf:
+            atom_pref_reshape = tf.reshape(atom_pref, [-1])
+            l2_pref_force_loss = tf.reduce_mean(
+                tf.multiply(tf.square(diff_f), atom_pref_reshape),
+                name="l2_pref_force_" + suffix,
+            )
+
+        if self.has_v:
+            virial_reshape = tf.reshape(virial, [-1])
+            virial_hat_reshape = tf.reshape(virial_hat, [-1])
+            l2_virial_loss = tf.reduce_mean(
+                tf.square(virial_hat_reshape - virial_reshape),
+                name="l2_virial_" + suffix,
+            )
+
+        if self.has_ae:
+            atom_ener_reshape = tf.reshape(atom_ener, [-1])
+            atom_ener_hat_reshape = tf.reshape(atom_ener_hat, [-1])
+            l2_atom_ener_loss = tf.reduce_mean(
+                tf.square(atom_ener_hat_reshape - atom_ener_reshape),
+                name="l2_atom_ener_" + suffix,
+            )
 
         atom_norm = 1.0 / global_cvt_2_tf_float(natoms[0])
         atom_norm_ener = 1.0 / global_cvt_2_ener_float(natoms[0])
@@ -192,34 +202,37 @@ def build(self, learning_rate, natoms, model_dict, label_dict, suffix):
         more_loss = {}
         if self.has_e:
             l2_loss += atom_norm_ener * (pref_e * l2_ener_loss)
-        more_loss["l2_ener_loss"] = l2_ener_loss
+            more_loss["l2_ener_loss"] = l2_ener_loss
         if self.has_f:
             l2_loss += global_cvt_2_ener_float(pref_f * l2_force_loss)
-        more_loss["l2_force_loss"] = l2_force_loss
+            more_loss["l2_force_loss"] = l2_force_loss
         if self.has_v:
             l2_loss += global_cvt_2_ener_float(atom_norm * (pref_v * l2_virial_loss))
-        more_loss["l2_virial_loss"] = l2_virial_loss
+            more_loss["l2_virial_loss"] = l2_virial_loss
         if self.has_ae:
             l2_loss += global_cvt_2_ener_float(pref_ae * l2_atom_ener_loss)
-        more_loss["l2_atom_ener_loss"] = l2_atom_ener_loss
+            more_loss["l2_atom_ener_loss"] = l2_atom_ener_loss
         if self.has_pf:
             l2_loss += global_cvt_2_ener_float(pref_pf * l2_pref_force_loss)
-        more_loss["l2_pref_force_loss"] = l2_pref_force_loss
+            more_loss["l2_pref_force_loss"] = l2_pref_force_loss
 
         # only used when tensorboard was set as true
         self.l2_loss_summary = tf.summary.scalar("l2_loss_" + suffix, tf.sqrt(l2_loss))
-        self.l2_loss_ener_summary = tf.summary.scalar(
-            "l2_ener_loss_" + suffix,
-            global_cvt_2_tf_float(tf.sqrt(l2_ener_loss))
-            / global_cvt_2_tf_float(natoms[0]),
-        )
-        self.l2_loss_force_summary = tf.summary.scalar(
-            "l2_force_loss_" + suffix, tf.sqrt(l2_force_loss)
-        )
-        self.l2_loss_virial_summary = tf.summary.scalar(
-            "l2_virial_loss_" + suffix,
-            tf.sqrt(l2_virial_loss) / global_cvt_2_tf_float(natoms[0]),
-        )
+        if self.has_e:
+            self.l2_loss_ener_summary = tf.summary.scalar(
+                "l2_ener_loss_" + suffix,
+                global_cvt_2_tf_float(tf.sqrt(l2_ener_loss))
+                / global_cvt_2_tf_float(natoms[0]),
+            )
+        if self.has_f:
+            self.l2_loss_force_summary = tf.summary.scalar(
+                "l2_force_loss_" + suffix, tf.sqrt(l2_force_loss)
+            )
+        if self.has_v:
+            self.l2_loss_virial_summary = tf.summary.scalar(
+                "l2_virial_loss_" + suffix,
+                tf.sqrt(l2_virial_loss) / global_cvt_2_tf_float(natoms[0]),
+            )
 
         self.l2_l = l2_loss
         self.l2_more = more_loss
diff --git a/deepmd/utils/argcheck.py b/deepmd/utils/argcheck.py
index 21bbcbb4cb..87ded2727c 100644
--- a/deepmd/utils/argcheck.py
+++ b/deepmd/utils/argcheck.py
@@ -374,6 +374,53 @@ def descrpt_se_atten_args():
     ]
 
 
+@descrpt_args_plugin.register("se_a_mask")
+def descrpt_se_a_mask_args():
+    doc_sel = 'This parameter sets the number of selected neighbors for each type of atom. It can be:\n\n\
+    - `List[int]`. The length of the list should be the same as the number of atom types in the system. `sel[i]` gives the selected number of type-i neighbors. `sel[i]` is recommended to be larger than the maximally possible number of type-i neighbors in the cut-off radius. It is noted that the total sel value must be less than 4096 in a GPU environment.\n\n\
+    - `str`. Can be "auto:factor" or "auto". "factor" is a float number larger than 1. This option will automatically determine the `sel`. In detail it counts the maximal number of neighbors with in the cutoff radius for each type of neighbor, then multiply the maximum by the "factor". Finally the number is wraped up to 4 divisible. The option "auto" is equivalent to "auto:1.1".'
+
+    doc_neuron = "Number of neurons in each hidden layers of the embedding net. When two layers are of the same size or one layer is twice as large as the previous layer, a skip connection is built."
+    doc_axis_neuron = "Size of the submatrix of G (embedding matrix)."
+    doc_activation_function = f'The activation function in the embedding net. Supported activation functions are {list_to_doc(ACTIVATION_FN_DICT.keys())} Note that "gelu" denotes the custom operator version, and "gelu_tf" denotes the TF standard version.'
+    doc_resnet_dt = 'Whether to use a "Timestep" in the skip connection'
+    doc_type_one_side = r"If true, the embedding network parameters vary by types of neighbor atoms only, so there will be $N_\text{types}$ sets of embedding network parameters. Otherwise, the embedding network parameters vary by types of centric atoms and types of neighbor atoms, so there will be $N_\text{types}^2$ sets of embedding network parameters."
+    doc_exclude_types = "The excluded pairs of types which have no interaction with each other. For example, `[[0, 1]]` means no interaction between type 0 and type 1."
+    doc_precision = f"The precision of the embedding net parameters, supported options are {list_to_doc(PRECISION_DICT.keys())} Default follows the interface precision."
+    doc_trainable = "If the parameters in the embedding net is trainable"
+    doc_seed = "Random seed for parameter initialization"
+
+    return [
+        Argument("sel", [list, str], optional=True, default="auto", doc=doc_sel),
+        Argument("neuron", list, optional=True, default=[10, 20, 40], doc=doc_neuron),
+        Argument(
+            "axis_neuron",
+            int,
+            optional=True,
+            default=4,
+            alias=["n_axis_neuron"],
+            doc=doc_axis_neuron,
+        ),
+        Argument(
+            "activation_function",
+            str,
+            optional=True,
+            default="tanh",
+            doc=doc_activation_function,
+        ),
+        Argument("resnet_dt", bool, optional=True, default=False, doc=doc_resnet_dt),
+        Argument(
+            "type_one_side", bool, optional=True, default=False, doc=doc_type_one_side
+        ),
+        Argument(
+            "exclude_types", list, optional=True, default=[], doc=doc_exclude_types
+        ),
+        Argument("precision", str, optional=True, default="default", doc=doc_precision),
+        Argument("trainable", bool, optional=True, default=True, doc=doc_trainable),
+        Argument("seed", [int, None], optional=True, doc=doc_seed),
+    ]
+
+
 def descrpt_variant_type_args(exclude_hybrid: bool = False) -> Variant:
     link_lf = make_link("loc_frame", "model/descriptor[loc_frame]")
     link_se_e2_a = make_link("se_e2_a", "model/descriptor[se_e2_a]")
@@ -389,6 +436,7 @@ def descrpt_variant_type_args(exclude_hybrid: bool = False) -> Variant:
 - `se_e3`: Used by the smooth edition of Deep Potential. The full relative coordinates are used to construct the descriptor. Three-body embedding will be used by this descriptor.\n\n\
 - `se_a_tpe`: Used by the smooth edition of Deep Potential. The full relative coordinates are used to construct the descriptor. Type embedding will be used by this descriptor.\n\n\
 - `se_atten`: Used by the smooth edition of Deep Potential. The full relative coordinates are used to construct the descriptor. Attention mechanism will be used by this descriptor.\n\n\
+- `se_a_mask`: Used by the smooth edition of Deep Potential. It can accept a variable number of atoms in a frame (Non-PBC system). *aparam* are required as an indicator matrix for the real/virtual sign of input atoms. \n\n\
 - `hybrid`: Concatenate of a list of descriptors as a new descriptor."
 
     return Variant("type", descrpt_args_plugin.get_all_argument(), doc=doc_descrpt_type)
@@ -415,6 +463,11 @@ def fitting_ener():
         "The shape of these layers should be the same. "
         "If null is given for a layer, parameters will not be shared."
     )
+    doc_use_aparam_as_mask = (
+        "Whether to use the aparam as a mask in input."
+        "If True, the aparam will not be used in fitting net for embedding."
+        "When descrpt is se_a_mask, the aparam will be used as a mask to indicate the input atom is real/virtual. And use_aparam_as_mask should be set to True."
+    )
 
     return [
         Argument("numb_fparam", int, optional=True, default=0, doc=doc_numb_fparam),
@@ -443,6 +496,13 @@ def fitting_ener():
         Argument("seed", [int, None], optional=True, doc=doc_seed),
         Argument("atom_ener", list, optional=True, default=[], doc=doc_atom_ener),
         Argument("layer_name", list, optional=True, doc=doc_layer_name),
+        Argument(
+            "use_aparam_as_mask",
+            bool,
+            optional=True,
+            default=False,
+            doc=doc_use_aparam_as_mask,
+        ),
     ]
 
 
diff --git a/doc/model/index.md b/doc/model/index.md
index 7b58d09ef8..343237eb92 100644
--- a/doc/model/index.md
+++ b/doc/model/index.md
@@ -5,6 +5,7 @@
 - [Descriptor `"se_e2_r"`](train-se-e2-r.md)
 - [Descriptor `"se_e3"`](train-se-e3.md)
 - [Descriptor `"se_atten"`](train-se-atten.md)
+- [Descriptor `"se_a_mask"`](train-se-a-mask.md)
 - [Descriptor `"hybrid"`](train-hybrid.md)
 - [Descriptor `sel`](sel.md)
 - [Fit energy](train-energy.md)
diff --git a/doc/model/index.rst b/doc/model/index.rst
index fab6673495..ca05a76e6d 100644
--- a/doc/model/index.rst
+++ b/doc/model/index.rst
@@ -14,5 +14,6 @@ Model
    train-energy
    train-fitting-tensor
    train-se-e2-a-tebd
+   train-se-a-mask
    dplr
    dprc
diff --git a/doc/model/overall.md b/doc/model/overall.md
index 437f3648f4..3d4052e464 100644
--- a/doc/model/overall.md
+++ b/doc/model/overall.md
@@ -20,8 +20,9 @@ DeePMD-kit implements the following descriptors:
 1. [`se_e2_a`](train-se-e2-a.md): DeepPot-SE constructed from all information (both angular and radial) of atomic configurations. The embedding takes the distance between atoms as input.
 2. [`se_e2_r`](train-se-e2-r.md): DeepPot-SE constructed from radial information of atomic configurations. The embedding takes the distance between atoms as input.
 3. [`se_e3`](train-se-e3.md): DeepPot-SE constructed from all information (both angular and radial) of atomic configurations. The embedding takes angles between two neighboring atoms as input.
-4. `loc_frame`: Defines a local frame at each atom and compute the descriptor as local coordinates under this frame.
-5. [`hybrid`](train-hybrid.md): Concate a list of descriptors to form a new descriptor.
+4. [`se_a_mask`](train-se-a-mask.md): DeepPot-SE constructed from all information (both angular and radial) of atomic configurations. The input frames in one system can have a varied number of atoms. Input particles are padded with virtual particles of the same length.
+5. `loc_frame`: Defines a local frame at each atom and compute the descriptor as local coordinates under this frame.
+6. [`hybrid`](train-hybrid.md): Concate a list of descriptors to form a new descriptor.
 
 The fitting of the following physical properties is supported
 1. [`ener`](train-energy.md): Fit the energy of the system. The force (derivative with atom positions) and the virial (derivative with the box tensor) can also be trained.
diff --git a/doc/model/train-se-a-mask.md b/doc/model/train-se-a-mask.md
new file mode 100644
index 0000000000..17c211ec73
--- /dev/null
+++ b/doc/model/train-se-a-mask.md
@@ -0,0 +1,75 @@
+# Descriptor `"se_a_mask"`
+
+
+Descriptor `se_a_mask` is a concise implementation of the descriptor `se_e2_a`,
+but functions slightly differently.
+`se_a_mask` is specially designed for DP/MM simulations where the number of atoms in DP regions is dynamically changed in simulations.
+
+Therefore, the descriptor `se_a_mask` is not supported for training with PBC systems for simplicity.
+Besides, to make the output shape of the descriptor matrix consistent,
+the input coordinates are padded with virtual particle coordinates to the maximum number of atoms (specified with `sel` in the descriptor setting) in the system.
+The real/virtual sign of the atoms is specified with the `aparam.npy` ( [ nframes * natoms ] ) file in the input systems set directory.
+The `aparam.npy` can also be seen as the mask of the atoms in the system,
+which is also the origin of the name `se_a_mask`.
+
+In this example, we will train a DP Mask model for zinc protein interactions.
+The input systems are the collection of zinc and its coordinates residues.
+A sample input system that contains 2 frames is included in the directory.
+```bash
+$deepmd_source_dir/examples/zinc_protein/data_dp_mask
+```
+A complete training input script of this example can be found in the directory.
+```bash
+$deepmd_source_dir/examples/zinc_protein/zinc_se_a_mask.json
+```
+
+The construction of the descriptor is given by section {ref}`descriptor <model/descriptor>`. An example of the descriptor is provided as follows
+```json
+	"descriptor" :{
+	    "type":	"se_a_mask",
+	    "sel":		[36, 16, 24, 64, 6, 1],
+	    "neuron":		[25, 50, 100],
+		"axis_neuron": 16,
+	    "type_one_side":	false,
+	    "resnet_dt":	false,
+	    "seed":		1
+	}
+```
+* The {ref}`type <model/descriptor/type>` of the descriptor is set to `"se_a_mask"`.
+* {ref}`sel <model/descriptor[se_a_mask]/sel>` gives the maximum number of atoms in input coordinates. It is a list, the length of which is the same as the number of atom types in the system, and `sel[i]` denotes the maximum number of atoms with type `i`.
+* The {ref}`neuron <model/descriptor[se_a_mask]/neuron>` specifies the size of the embedding net. From left to right the members denote the sizes of each hidden layer from the input end to the output end, respectively. If the outer layer is twice the size of the inner layer, then the inner layer is copied and concatenated, then a [ResNet architecture](https://arxiv.org/abs/1512.03385) is built between them.
+* The {ref}`axis_neuron <model/descriptor[se_a_mask]/axis_neuron>` specifies the size of the submatrix of the embedding matrix, the axis matrix as explained in the [DeepPot-SE paper](https://arxiv.org/abs/1805.09003)
+* If the option {ref}`type_one_side <model/descriptor[se_a_mask]/type_one_side>` is set to `true`, the embedding network parameters vary by types of neighbor atoms only, so there will be $N_\text{types}$ sets of embedding network parameters. Otherwise, the embedding network parameters vary by types of centric atoms and types of neighbor atoms, so there will be $N_\text{types}^2$ sets of embedding network parameters.
+* If the option {ref}`resnet_dt <model/descriptor[se_a_mask]/resnet_dt>` is set to `true`, then a timestep is used in the ResNet.
+* {ref}`seed <model/descriptor[se_a_mask]/seed>` gives the random seed that is used to generate random numbers when initializing the model parameters.
+
+To make the `aparam.npy` used for descriptor `se_a_mask`, two variables in `fitting_net` section are needed.
+```json
+	"fitting_net" :{
+	    "neuron": [240, 240, 240],
+      	"resnet_dt": true,
+      	"seed": 1,
+      	"numb_aparam": 1,
+      	"use_aparam_as_mask": true
+	}
+```
+* `neuron`, `resnet_dt` and `seed` are the same as the {ref}`fitting_net <model/fitting_net[ener]>` section for fitting energy.
+* {ref}`numb_aparam <model/fitting_net[ener]/numb_aparam>` gives the dimesion of the `aparam.npy` file. In this example, it is set to 1 and stores the real/virtual sign of the atoms. For real/virtual atoms, the corresponding sign in `aparam.npy` is set to 1/0.
+* {ref}`use_aparam_as_mask <model/fitting_net[ener]/use_aparam_as_mask>` is set to `true` to use the `aparam.npy` as the mask of the atoms in the descriptor `se_a_mask`.
+
+Finally, to make a reasonable fitting task with `se_a_mask` descriptor for DP/MM simulations, the loss function with `se_a_mask` is designed to include the atomic forces difference in specific atoms of the input particles only.
+More details about the selection of the specific atoms can be found in paper [DP/MM](left to be filled).
+Thus, `atom_pref.npy` ( [ nframes * natoms ] ) is required as the indicator of the specific atoms in the input particles.
+And the `loss` section in the training input script should be set as follows.
+```json
+"loss": {
+    "type": "ener",
+    "start_pref_e": 0.0,
+    "limit_pref_e": 0.0,
+    "start_pref_f": 0.0,
+    "limit_pref_f": 0.0,
+    "start_pref_pf": 1.0,
+    "limit_pref_pf": 1.0,
+    "_comment": " that's all"
+  }
+```
diff --git a/dp4mask.pb b/dp4mask.pb
new file mode 100644
index 0000000000..45eac75cbd
Binary files /dev/null and b/dp4mask.pb differ
diff --git a/examples/zinc_protein/data_dp_mask/nopbc b/examples/zinc_protein/data_dp_mask/nopbc
new file mode 100644
index 0000000000..e69de29bb2
diff --git a/examples/zinc_protein/data_dp_mask/set.000/aparam.npy b/examples/zinc_protein/data_dp_mask/set.000/aparam.npy
new file mode 100644
index 0000000000..85d2f0800c
Binary files /dev/null and b/examples/zinc_protein/data_dp_mask/set.000/aparam.npy differ
diff --git a/examples/zinc_protein/data_dp_mask/set.000/atom_pref.npy b/examples/zinc_protein/data_dp_mask/set.000/atom_pref.npy
new file mode 100644
index 0000000000..02cca0c60d
Binary files /dev/null and b/examples/zinc_protein/data_dp_mask/set.000/atom_pref.npy differ
diff --git a/examples/zinc_protein/data_dp_mask/set.000/box.npy b/examples/zinc_protein/data_dp_mask/set.000/box.npy
new file mode 100644
index 0000000000..71a7dde5ec
Binary files /dev/null and b/examples/zinc_protein/data_dp_mask/set.000/box.npy differ
diff --git a/examples/zinc_protein/data_dp_mask/set.000/coord.npy b/examples/zinc_protein/data_dp_mask/set.000/coord.npy
new file mode 100644
index 0000000000..f3f86b9622
Binary files /dev/null and b/examples/zinc_protein/data_dp_mask/set.000/coord.npy differ
diff --git a/examples/zinc_protein/data_dp_mask/set.000/energy.npy b/examples/zinc_protein/data_dp_mask/set.000/energy.npy
new file mode 100644
index 0000000000..2861a0836c
Binary files /dev/null and b/examples/zinc_protein/data_dp_mask/set.000/energy.npy differ
diff --git a/examples/zinc_protein/data_dp_mask/set.000/force.npy b/examples/zinc_protein/data_dp_mask/set.000/force.npy
new file mode 100644
index 0000000000..e6536f07ba
Binary files /dev/null and b/examples/zinc_protein/data_dp_mask/set.000/force.npy differ
diff --git a/examples/zinc_protein/data_dp_mask/type.raw b/examples/zinc_protein/data_dp_mask/type.raw
new file mode 100644
index 0000000000..7b829b7f16
--- /dev/null
+++ b/examples/zinc_protein/data_dp_mask/type.raw
@@ -0,0 +1,147 @@
+0
+0
+0
+0
+0
+0
+0
+0
+0
+0
+0
+0
+0
+0
+0
+0
+0
+0
+0
+0
+0
+0
+0
+0
+0
+0
+0
+0
+0
+0
+0
+0
+0
+0
+0
+0
+1
+1
+1
+1
+1
+1
+1
+1
+1
+1
+1
+1
+1
+1
+1
+1
+2
+2
+2
+2
+2
+2
+2
+2
+2
+2
+2
+2
+2
+2
+2
+2
+2
+2
+2
+2
+2
+2
+2
+2
+3
+3
+3
+3
+3
+3
+3
+3
+3
+3
+3
+3
+3
+3
+3
+3
+3
+3
+3
+3
+3
+3
+3
+3
+3
+3
+3
+3
+3
+3
+3
+3
+3
+3
+3
+3
+3
+3
+3
+3
+3
+3
+3
+3
+3
+3
+3
+3
+3
+3
+3
+3
+3
+3
+3
+3
+3
+3
+3
+3
+3
+3
+3
+3
+4
+4
+4
+4
+4
+4
+5
diff --git a/examples/zinc_protein/data_dp_mask/type_map.raw b/examples/zinc_protein/data_dp_mask/type_map.raw
new file mode 100644
index 0000000000..9b7782b7fb
--- /dev/null
+++ b/examples/zinc_protein/data_dp_mask/type_map.raw
@@ -0,0 +1,6 @@
+C
+O
+N
+H
+S
+ZN
diff --git a/examples/zinc_protein/zinc_se_a_mask.json b/examples/zinc_protein/zinc_se_a_mask.json
new file mode 100644
index 0000000000..f0bf5ab0d6
--- /dev/null
+++ b/examples/zinc_protein/zinc_se_a_mask.json
@@ -0,0 +1,85 @@
+{
+  "_comment": " model parameters",
+  "model": {
+    "type_map": [
+      "C",
+      "O",
+      "N",
+      "H",
+      "S",
+      "ZN"
+    ],
+    "descriptor": {
+      "type": "se_a_mask",
+      "sel": [
+        36,
+        16,
+        24,
+        64,
+        6,
+        1
+      ],
+      "neuron": [
+        32,
+        32,
+        64,
+        128
+      ],
+      "resnet_dt": true,
+      "axis_neuron": 16,
+      "seed": 1,
+      "_comment": " that's all"
+    },
+    "fitting_net": {
+      "neuron": [
+        240,
+        240,
+        240
+      ],
+      "resnet_dt": true,
+      "seed": 1,
+      "numb_aparam": 1,
+      "use_aparam_as_mask": true,
+      "_comment": " that's all"
+    },
+    "_comment": " that's all"
+  },
+
+  "learning_rate": {
+    "type": "exp",
+    "decay_steps": 20000,
+    "start_lr": 0.001,
+    "stop_lr": 3.51e-8,
+    "_comment": "that's all"
+  },
+
+  "loss": {
+    "type": "ener",
+    "start_pref_e": 0.0,
+    "limit_pref_e": 0.0,
+    "start_pref_f": 0.0,
+    "limit_pref_f": 0.0,
+    "start_pref_pf": 1.0,
+    "limit_pref_pf": 1.0,
+    "_comment": " that's all"
+  },
+  "training": {
+    "validation_data": {
+      "systems": [
+        "example/zinc_protein/data_dp_mask/"
+      ],
+      "batch_size": 2,
+      "numb_btch": 1,
+      "_comment": "that's all"
+    },
+    "numb_steps": 1,
+    "seed": 10,
+    "disp_freq": 100,
+    "save_freq": 1000,
+    "tensorboard": true,
+    "tensorboard_log_dir": "log4tensorboard",
+    "tensorboard_freq": 100,
+    "_comment": "that's all"
+  },
+  "_comment": "that's all"
+}
diff --git a/source/op/CMakeLists.txt b/source/op/CMakeLists.txt
index 4377944cbe..fdc7fa7ea2 100644
--- a/source/op/CMakeLists.txt
+++ b/source/op/CMakeLists.txt
@@ -23,9 +23,11 @@ file(
   descrpt_se_a_ef.cc
   descrpt_se_a_ef_para.cc
   descrpt_se_a_ef_vert.cc
+  descrpt_se_a_mask.cc
   pair_tab.cc
   prod_force_multi_device.cc
   prod_virial_multi_device.cc
+  prod_force_se_a_mask.cc
   soft_min.cc
   soft_min_force.cc
   soft_min_virial.cc
@@ -42,6 +44,7 @@ file(
   custom_op.cc
   prod_force_grad.cc
   prod_force_grad_multi_device.cc
+  prod_force_se_a_mask_grad.cc
   prod_virial_grad.cc
   prod_virial_grad_multi_device.cc
   soft_min_force_grad.cc
diff --git a/source/op/_prod_force_se_a_mask_grad.py b/source/op/_prod_force_se_a_mask_grad.py
new file mode 100644
index 0000000000..4dc83cbc48
--- /dev/null
+++ b/source/op/_prod_force_se_a_mask_grad.py
@@ -0,0 +1,25 @@
+#!/usr/bin/env python3
+"""
+Gradients for prod force se_a_mask.
+"""
+
+from tensorflow.python.framework import (
+    ops,
+)
+
+from deepmd.env import (
+    op_grads_module,
+)
+
+
+@ops.RegisterGradient("ProdForceSeAMask")
+def _prod_force_se_a_mask_grad_cc(op, grad):
+    net_grad = op_grads_module.prod_force_se_a_mask_grad(
+        grad,
+        op.inputs[0],
+        op.inputs[1],
+        op.inputs[2],
+        op.inputs[3],
+        total_atom_num=op.get_attr("total_atom_num"),
+    )
+    return [net_grad, None, None, None]
diff --git a/source/op/descrpt_se_a_mask.cc b/source/op/descrpt_se_a_mask.cc
new file mode 100644
index 0000000000..73d8bb83ca
--- /dev/null
+++ b/source/op/descrpt_se_a_mask.cc
@@ -0,0 +1,352 @@
+
+#include <cmath>
+
+#include "ComputeDescriptor.h"
+#include "custom_op.h"
+#include "errors.h"
+#include "fmt_nlist.h"
+#include "neighbor_list.h"
+
+typedef double boxtensor_t;
+typedef double compute_t;
+
+REGISTER_OP("DescrptSeAMask")
+    .Attr("T: {float, double} = DT_DOUBLE")
+    .Input("coord: T")
+    .Input("type: int32")
+    .Input("mask: int32")
+    .Input("box: T")         // Not used in practice
+    .Input("natoms: int32")  // Used to fetch total_atom_num and check the size
+                             // of input.
+    .Input("mesh: int32")    // Not used in practice
+    .Output("descrpt: T")
+    .Output("descrpt_deriv: T")
+    .Output("rij: T")
+    .Output("nlist: int32");
+
+template <typename FPTYPE>
+struct NeighborInfo {
+  int type;
+  FPTYPE dist;
+  int index;
+  NeighborInfo() : type(0), dist(0), index(0) {}
+  NeighborInfo(int tt, FPTYPE dd, int ii) : type(tt), dist(dd), index(ii) {}
+  bool operator<(const NeighborInfo &b) const {
+    return (type < b.type ||
+            (type == b.type &&
+             (dist < b.dist || (dist == b.dist && index < b.index))));
+  }
+};
+
+template <typename Device, typename FPTYPE>
+class DescrptSeAMaskOp : public OpKernel {
+ public:
+  explicit DescrptSeAMaskOp(OpKernelConstruction *context) : OpKernel(context) {
+    // OP_REQUIRES_OK(context);
+  }
+
+  void Compute(OpKernelContext *context) override {
+    deepmd::safe_compute(
+        context, [this](OpKernelContext *context) { this->_Compute(context); });
+  }
+
+  void _Compute(OpKernelContext *context) {
+    // Grab the input tensor
+    int context_input_index = 0;
+    const Tensor &coord_tensor = context->input(context_input_index++);
+    const Tensor &type_tensor = context->input(context_input_index++);
+    const Tensor &mask_matrix_tensor = context->input(context_input_index++);
+    const Tensor &box_tensor = context->input(context_input_index++);
+    const Tensor &natoms_tensor = context->input(context_input_index++);
+    const Tensor &mesh_tensor = context->input(context_input_index++);
+
+    // set size of the sample
+    OP_REQUIRES(context, (coord_tensor.shape().dims() == 2),
+                errors::InvalidArgument("Dim of coord should be 2"));
+    OP_REQUIRES(
+        context, (type_tensor.shape().dims() == 2),
+        errors::InvalidArgument("Dim of type for se_e2_a_mask op should be 2"));
+    OP_REQUIRES(context, (mask_matrix_tensor.shape().dims() == 2),
+                errors::InvalidArgument("Dim of mask matrix should be 2"));
+
+    int nsamples = coord_tensor.shape().dim_size(0);
+
+    // check the sizes
+    OP_REQUIRES(context, (nsamples == type_tensor.shape().dim_size(0)),
+                errors::InvalidArgument("number of samples should match"));
+    OP_REQUIRES(context, (nsamples == mask_matrix_tensor.shape().dim_size(0)),
+                errors::InvalidArgument("number of samples should match"));
+
+    // Set n_descrpt for each atom. Include 1/rr, cos(theta), cos(phi), sin(phi)
+    int n_descrpt = 4;
+
+    // Calculate the total_atom_num
+    auto natoms = natoms_tensor.flat<int>();
+    total_atom_num = natoms(1);
+    // check the sizes
+    OP_REQUIRES(context,
+                (total_atom_num * 3 == coord_tensor.shape().dim_size(1)),
+                errors::InvalidArgument("number of atoms should match"));
+    OP_REQUIRES(context,
+                (total_atom_num == mask_matrix_tensor.shape().dim_size(1)),
+                errors::InvalidArgument("number of atoms should match"));
+
+    // Create an output tensor
+    TensorShape descrpt_shape;
+    descrpt_shape.AddDim(nsamples);
+    descrpt_shape.AddDim(total_atom_num * total_atom_num * n_descrpt);
+    TensorShape descrpt_deriv_shape;
+    descrpt_deriv_shape.AddDim(nsamples);
+    descrpt_deriv_shape.AddDim(total_atom_num * total_atom_num * n_descrpt * 3);
+    TensorShape rij_shape;
+    rij_shape.AddDim(nsamples);
+    rij_shape.AddDim(total_atom_num * total_atom_num * 3);
+    TensorShape nlist_shape;
+    nlist_shape.AddDim(nsamples);
+    nlist_shape.AddDim(total_atom_num * total_atom_num);
+
+    int context_output_index = 0;
+    Tensor *descrpt_tensor = NULL;
+    OP_REQUIRES_OK(
+        context, context->allocate_output(context_output_index++, descrpt_shape,
+                                          &descrpt_tensor));
+    Tensor *descrpt_deriv_tensor = NULL;
+    OP_REQUIRES_OK(context, context->allocate_output(context_output_index++,
+                                                     descrpt_deriv_shape,
+                                                     &descrpt_deriv_tensor));
+    Tensor *rij_tensor = NULL;
+    OP_REQUIRES_OK(context, context->allocate_output(context_output_index++,
+                                                     rij_shape, &rij_tensor));
+    Tensor *nlist_tensor = NULL;
+    OP_REQUIRES_OK(context,
+                   context->allocate_output(context_output_index++, nlist_shape,
+                                            &nlist_tensor));
+
+    auto coord = coord_tensor.matrix<FPTYPE>();
+    auto type = type_tensor.matrix<int>();
+    auto mask_matrix = mask_matrix_tensor.matrix<int>();
+
+    auto descrpt = descrpt_tensor->matrix<FPTYPE>();
+    auto descrpt_deriv = descrpt_deriv_tensor->matrix<FPTYPE>();
+    auto rij = rij_tensor->matrix<FPTYPE>();
+    auto nlist = nlist_tensor->matrix<int>();
+
+    // // check the type
+    // int max_type_v = 0;
+    // for (int ii = 0; ii < natoms; ++ii){
+    //   if (type(0, ii) > max_type_v) max_type_v = type(0, ii);
+    // }
+    // int ntype = max_type_v + 1;
+
+    // loop over atoms, compute descriptors for each atom
+#pragma omp parallel for
+    for (int kk = 0; kk < nsamples; ++kk) {
+      // Iterate for each frame.
+      int nloc = total_atom_num;
+      int natoms = total_atom_num;
+
+      std::vector<compute_t> d_coord3(natoms * 3);
+      for (int ii = 0; ii < natoms; ++ii) {
+        for (int dd = 0; dd < 3; ++dd) {
+          d_coord3[ii * 3 + dd] = coord(kk, ii * 3 + dd);
+        }
+      }
+
+      std::vector<int> d_type(natoms);
+      for (int ii = 0; ii < natoms; ++ii) {
+        d_type[ii] = type(kk, ii);
+      }
+
+      std::vector<int> d_mask(natoms);
+      for (int ii = 0; ii < natoms; ++ii) {
+        d_mask[ii] = mask_matrix(kk, ii);
+      }
+      std::vector<int> sorted_nlist(total_atom_num);
+
+      for (int ii = 0; ii < nloc; ii++) {
+        // Check this atom is virtual atom or not. If it is, set the virtual
+        // atom's environment descriptor and derivation on descriptor to be zero
+        // directly.
+        if (mask_matrix(kk, ii) == 0) {
+          for (int jj = 0; jj < natoms * 4; ++jj) {
+            descrpt(kk, ii * total_atom_num * 4 + jj) = 0.;
+          }
+          for (int jj = 0; jj < natoms * 4 * 3; ++jj) {
+            descrpt_deriv(kk, ii * total_atom_num * 4 * 3 + jj) = 0.;
+          }
+          // Save the neighbor list relative coordinates with center atom ii.
+          for (int jj = 0; jj < natoms * 3; ++jj) {
+            rij(kk, ii * natoms * 3 + jj) = 0.;
+          }
+          // Save the neighbor atoms indicies.
+          for (int jj = 0; jj < natoms; jj++) {
+            nlist(kk, ii * natoms + jj) = -1;
+          }
+          continue;
+        }
+
+        // Build the neighbor list for atom ii.
+        std::fill(sorted_nlist.begin(), sorted_nlist.end(), -1);
+        buildAndSortNeighborList(ii, d_coord3, d_type, d_mask, sorted_nlist,
+                                 total_atom_num);
+
+        // Set the center atom coordinates.
+        std::vector<compute_t> rloc(3);
+        for (int dd = 0; dd < 3; ++dd) {
+          rloc[dd] = coord(kk, ii * 3 + dd);
+        }
+
+        // Compute the descriptor and derive for the descriptor for each atom.
+        std::vector<compute_t> descrpt_atom(natoms * 4);
+        std::vector<compute_t> descrpt_deriv_atom(natoms * 12);
+        std::vector<compute_t> rij_atom(natoms * 3);
+
+        std::fill(descrpt_deriv_atom.begin(), descrpt_deriv_atom.end(), 0.0);
+        std::fill(descrpt_atom.begin(), descrpt_atom.end(), 0.0);
+        std::fill(rij_atom.begin(), rij_atom.end(), 0.0);
+
+        // Compute the each environment std::vector for each atom.
+        for (int jj = 0; jj < natoms; jj++) {
+          int j_idx = sorted_nlist[jj];
+
+          compute_t temp_rr;
+          compute_t temp_diff[3];
+          temp_rr = 0.;
+
+          // Once ii == j_idx, the descriptor and derivation should be set to
+          // zero. Or if the atom jj is an virtual atom. The descriptor and
+          // derivation should be zero also.
+          if (ii == j_idx || mask_matrix(kk, j_idx) == 0) {
+            // 1./rr, cos(theta), cos(phi), sin(phi)
+            descrpt_atom[jj * 4 + 0] = 0.;
+            descrpt_atom[jj * 4 + 1] = 0.;
+            descrpt_atom[jj * 4 + 2] = 0.;
+            descrpt_atom[jj * 4 + 3] = 0.;
+            // derive of the component 1/r
+            descrpt_deriv_atom[jj * 12 + 0] = 0.;
+            descrpt_deriv_atom[jj * 12 + 1] = 0.;
+            descrpt_deriv_atom[jj * 12 + 2] = 0.;
+            // derive of the component x/r2
+            descrpt_deriv_atom[jj * 12 + 3] = 0.;  // on x.
+            descrpt_deriv_atom[jj * 12 + 4] = 0.;  // on y.
+            descrpt_deriv_atom[jj * 12 + 5] = 0.;  // on z.
+            // derive of the component y/r2
+            descrpt_deriv_atom[jj * 12 + 6] = 0.;  // on x.
+            descrpt_deriv_atom[jj * 12 + 7] = 0.;  // on y.
+            descrpt_deriv_atom[jj * 12 + 8] = 0.;  // on z.
+            // derive of the component z/r2
+            descrpt_deriv_atom[jj * 12 + 9] = 0.;   // on x.
+            descrpt_deriv_atom[jj * 12 + 10] = 0.;  // on y.
+            descrpt_deriv_atom[jj * 12 + 11] = 0.;  // on z.
+            rij_atom[jj * 3 + 0] = 0.;
+            rij_atom[jj * 3 + 1] = 0.;
+            rij_atom[jj * 3 + 2] = 0.;
+            continue;
+          }
+
+          for (int dd = 0; dd < 3; dd++) {
+            temp_diff[dd] = d_coord3[j_idx * 3 + dd] - rloc[dd];
+            rij_atom[jj * 3 + dd] = temp_diff[dd];
+          }
+
+          temp_rr = deepmd::dot3<compute_t>(temp_diff, temp_diff);
+
+          compute_t x = temp_diff[0];
+          compute_t y = temp_diff[1];
+          compute_t z = temp_diff[2];
+
+          // r^2
+          compute_t nr2 = temp_rr;
+          // 1/r
+          compute_t inr = 1. / sqrt(nr2);
+          // r
+          compute_t nr = nr2 * inr;
+          // 1/r^2
+          compute_t inr2 = inr * inr;
+          // 1/r^4
+          compute_t inr4 = inr2 * inr2;
+          // 1/r^3
+          compute_t inr3 = inr * inr2;
+          // 1./rr, cos(theta), cos(phi), sin(phi)
+          descrpt_atom[jj * 4 + 0] = 1. / nr;
+          descrpt_atom[jj * 4 + 1] = x / nr2;
+          descrpt_atom[jj * 4 + 2] = y / nr2;
+          descrpt_atom[jj * 4 + 3] = z / nr2;
+          // derive of the component 1/r
+          descrpt_deriv_atom[jj * 12 + 0] = x * inr3;
+          descrpt_deriv_atom[jj * 12 + 1] = y * inr3;
+          descrpt_deriv_atom[jj * 12 + 2] = z * inr3;
+          // derive of the component x/r2
+          descrpt_deriv_atom[jj * 12 + 3] = 2. * x * x * inr4 - inr2;  // on x.
+          descrpt_deriv_atom[jj * 12 + 4] = 2. * x * y * inr4;         // on y.
+          descrpt_deriv_atom[jj * 12 + 5] = 2. * x * z * inr4;         // on z.
+          // derive of the component y/r2
+          descrpt_deriv_atom[jj * 12 + 6] = 2. * y * x * inr4;         // on x.
+          descrpt_deriv_atom[jj * 12 + 7] = 2. * y * y * inr4 - inr2;  // on y.
+          descrpt_deriv_atom[jj * 12 + 8] = 2. * y * z * inr4;         // on z.
+          // derive of the component z/r2
+          descrpt_deriv_atom[jj * 12 + 9] = 2. * z * x * inr4;          // on x.
+          descrpt_deriv_atom[jj * 12 + 10] = 2. * z * y * inr4;         // on y.
+          descrpt_deriv_atom[jj * 12 + 11] = 2. * z * z * inr4 - inr2;  // on z.
+        }
+
+        for (int jj = 0; jj < natoms * 4; ++jj) {
+          descrpt(kk, ii * total_atom_num * 4 + jj) = descrpt_atom[jj];
+        }
+        for (int jj = 0; jj < natoms * 4 * 3; ++jj) {
+          descrpt_deriv(kk, ii * total_atom_num * 4 * 3 + jj) =
+              descrpt_deriv_atom[jj];
+        }
+        // Save the neighbor list relative coordinates with center atom ii.
+        for (int jj = 0; jj < natoms * 3; ++jj) {
+          rij(kk, ii * natoms * 3 + jj) = rij_atom[jj];
+        }
+        // Save the neighbor atoms indicies.
+        for (int jj = 0; jj < natoms; ++jj) {
+          nlist(kk, ii * natoms + jj) = sorted_nlist[jj];
+        }
+      }
+    }
+  }
+
+ private:
+  int total_atom_num;
+  compute_t max_distance = 10000.0;
+  void buildAndSortNeighborList(int i_idx,
+                                const std::vector<compute_t> d_coord3,
+                                std::vector<int> &d_type,
+                                std::vector<int> &d_mask,
+                                std::vector<int> &sorted_nlist,
+                                int total_atom_num) {
+    // sorted_nlist.resize(total_atom_num);
+    std::vector<NeighborInfo<double>> sel_nei;
+    for (int jj = 0; jj < total_atom_num; jj++) {
+      compute_t diff[3];
+      const int j_idx = jj;
+      for (int dd = 0; dd < 3; ++dd) {
+        diff[dd] = d_coord3[j_idx * 3 + dd] - d_coord3[i_idx * 3 + dd];
+      }
+      // Check if j_idx atom is virtual particle or not.
+      compute_t rr = 0.0;
+      if (d_mask[j_idx] == 0 || j_idx == i_idx) {
+        rr = max_distance;
+      } else {
+        rr = sqrt(deepmd::dot3<compute_t>(diff, diff));
+      }
+      sel_nei.push_back(NeighborInfo<double>(d_type[j_idx], rr, j_idx));
+    }
+    std::sort(sel_nei.begin(), sel_nei.end());
+    // Save the sorted atom index.
+    for (int jj = 0; jj < sel_nei.size(); jj++) {
+      int atom_idx = sel_nei[jj].index;
+      sorted_nlist[jj] = atom_idx;
+    }
+  }
+};
+
+#define REGISTER_CPU(T)                                                 \
+  REGISTER_KERNEL_BUILDER(                                              \
+      Name("DescrptSeAMask").Device(DEVICE_CPU).TypeConstraint<T>("T"), \
+      DescrptSeAMaskOp<CPUDevice, T>);
+REGISTER_CPU(float);
+REGISTER_CPU(double);
diff --git a/source/op/prod_force_se_a_mask.cc b/source/op/prod_force_se_a_mask.cc
new file mode 100644
index 0000000000..1859859a8a
--- /dev/null
+++ b/source/op/prod_force_se_a_mask.cc
@@ -0,0 +1,153 @@
+#include "custom_op.h"
+
+REGISTER_OP("ProdForceSeAMask")
+    .Attr("T: {float, double} = DT_DOUBLE")
+    .Input("net_deriv: T")
+    .Input("in_deriv: T")
+    .Input("mask: int32")
+    .Input("nlist: int32")
+    .Attr("total_atom_num: int")
+    .Output("force: T");
+
+using namespace tensorflow;
+
+using CPUDevice = Eigen::ThreadPoolDevice;
+
+template <typename Device, typename FPTYPE>
+class ProdForceSeAMaskOp : public OpKernel {
+ public:
+  explicit ProdForceSeAMaskOp(OpKernelConstruction *context)
+      : OpKernel(context) {
+    OP_REQUIRES_OK(context,
+                   context->GetAttr("total_atom_num", &total_atom_num));
+  }
+
+  void Compute(OpKernelContext *context) override {
+    deepmd::safe_compute(
+        context, [this](OpKernelContext *context) { this->_Compute(context); });
+  }
+
+  void _Compute(OpKernelContext *context) {
+    // Grab the input tensor
+    const Tensor &net_deriv_tensor = context->input(0);
+    const Tensor &in_deriv_tensor = context->input(1);
+    const Tensor &mask_tensor = context->input(2);
+    const Tensor &nlist_tensor = context->input(3);
+
+    // set size of the sample
+    OP_REQUIRES(context, (net_deriv_tensor.shape().dims() == 2),
+                errors::InvalidArgument("Dim of net deriv should be 2"));
+    OP_REQUIRES(context, (in_deriv_tensor.shape().dims() == 2),
+                errors::InvalidArgument("Dim of input deriv should be 2"));
+    OP_REQUIRES(context, (mask_tensor.shape().dims() == 2),
+                errors::InvalidArgument("Dim of mask matrix should be 2"));
+    OP_REQUIRES(context, (nlist_tensor.shape().dims() == 2),
+                errors::InvalidArgument("Dim of nlist should be 2"));
+
+    int nframes = net_deriv_tensor.shape().dim_size(0);
+    int nloc = total_atom_num;
+    int nall = total_atom_num;
+    int ndescrpt = nall * 4;
+    int nnei = nlist_tensor.shape().dim_size(1) / nloc;
+
+    // check the sizes
+    OP_REQUIRES(context, (nframes == in_deriv_tensor.shape().dim_size(0)),
+                errors::InvalidArgument("number of samples should match"));
+    OP_REQUIRES(context, (nframes == nlist_tensor.shape().dim_size(0)),
+                errors::InvalidArgument("number of samples should match"));
+    OP_REQUIRES(context,
+                (nloc * ndescrpt * 3 == in_deriv_tensor.shape().dim_size(1)),
+                errors::InvalidArgument("number of descriptors should match"));
+
+    // Create an output tensor
+    TensorShape force_shape;
+    force_shape.AddDim(nframes);
+    force_shape.AddDim(3 * nall);
+    // std::cout << "forcesahpe " << force_shape.dim_size(0) << " " <<
+    // force_shape.dim_size(1) << std::endl;
+    Tensor *force_tensor = NULL;
+    OP_REQUIRES_OK(context,
+                   context->allocate_output(0, force_shape, &force_tensor));
+
+    // flat the tensors
+    auto net_deriv = net_deriv_tensor.flat<FPTYPE>();
+    auto in_deriv = in_deriv_tensor.flat<FPTYPE>();
+    auto nlist = nlist_tensor.flat<int>();
+    auto mask = mask_tensor.flat<int>();
+    auto force = force_tensor->flat<FPTYPE>();
+
+// loop over samples
+#pragma omp parallel for
+    for (int kk = 0; kk < nframes; ++kk) {
+      int natoms = total_atom_num;
+      int nloc = natoms;
+
+      int force_iter = kk * natoms * 3;
+      int net_iter = kk * natoms * ndescrpt;
+      int in_iter = kk * natoms * ndescrpt * 3;
+      int mask_iter = kk * natoms;
+      int nlist_iter = kk * natoms * natoms;
+
+      for (int ii = 0; ii < natoms; ii++) {
+        int i_idx = ii;
+        force(force_iter + i_idx * 3 + 0) = 0.0;
+        force(force_iter + i_idx * 3 + 1) = 0.0;
+        force(force_iter + i_idx * 3 + 2) = 0.0;
+      }
+
+      for (int ii = 0; ii < natoms; ii++) {
+        int i_idx = ii;
+        // Check if the atom ii is virtual particle or not.
+        if (mask(mask_iter + i_idx) == 0) {
+          continue;
+        }
+        // derivation with center atom. (x_j - x_i). x_i is the center atom.
+        // Derivation with center atom.
+        for (int aa = 0; aa < natoms * 4; ++aa) {
+          force(force_iter + i_idx * 3 + 0) -=
+              net_deriv(net_iter + i_idx * ndescrpt + aa) *
+              in_deriv(in_iter + i_idx * ndescrpt * 3 + aa * 3 + 0);
+          force(force_iter + i_idx * 3 + 1) -=
+              net_deriv(net_iter + i_idx * ndescrpt + aa) *
+              in_deriv(in_iter + i_idx * ndescrpt * 3 + aa * 3 + 1);
+          force(force_iter + i_idx * 3 + 2) -=
+              net_deriv(net_iter + i_idx * ndescrpt + aa) *
+              in_deriv(in_iter + i_idx * ndescrpt * 3 + aa * 3 + 2);
+        }
+        // Derivation with other atom.
+        for (int jj = 0; jj < natoms; jj++) {
+          // Get the neighbor index from nlist tensor.
+          int j_idx = nlist(nlist_iter + i_idx * natoms + jj);
+
+          if (j_idx == i_idx) {
+            continue;
+          }
+          int aa_start, aa_end;
+          aa_start = jj * 4;
+          aa_end = jj * 4 + 4;
+          for (int aa = aa_start; aa < aa_end; aa++) {
+            force(force_iter + j_idx * 3 + 0) +=
+                net_deriv(net_iter + i_idx * ndescrpt + aa) *
+                in_deriv(in_iter + i_idx * ndescrpt * 3 + aa * 3 + 0);
+            force(force_iter + j_idx * 3 + 1) +=
+                net_deriv(net_iter + i_idx * ndescrpt + aa) *
+                in_deriv(in_iter + i_idx * ndescrpt * 3 + aa * 3 + 1);
+            force(force_iter + j_idx * 3 + 2) +=
+                net_deriv(net_iter + i_idx * ndescrpt + aa) *
+                in_deriv(in_iter + i_idx * ndescrpt * 3 + aa * 3 + 2);
+          }
+        }
+      }
+    }
+  }
+
+ private:
+  int total_atom_num;
+};
+
+#define REGISTER_CPU(T)                                                   \
+  REGISTER_KERNEL_BUILDER(                                                \
+      Name("ProdForceSeAMask").Device(DEVICE_CPU).TypeConstraint<T>("T"), \
+      ProdForceSeAMaskOp<CPUDevice, T>);
+REGISTER_CPU(float);
+REGISTER_CPU(double);
diff --git a/source/op/prod_force_se_a_mask_grad.cc b/source/op/prod_force_se_a_mask_grad.cc
new file mode 100644
index 0000000000..b19f8d5db6
--- /dev/null
+++ b/source/op/prod_force_se_a_mask_grad.cc
@@ -0,0 +1,162 @@
+#include "custom_op.h"
+
+REGISTER_OP("ProdForceSeAMaskGrad")
+    .Attr("T: {float, double} = DT_DOUBLE")
+    .Input("grad: T")
+    .Input("net_deriv: T")
+    .Input("in_deriv: T")
+    .Input("mask: int32")
+    .Input("nlist: int32")
+    .Attr("total_atom_num: int")
+    .Output("grad_net: T");
+
+using CPUDevice = Eigen::ThreadPoolDevice;
+
+template <typename Device, typename FPTYPE>
+class ProdForceSeAMaskGradOp : public OpKernel {
+ public:
+  explicit ProdForceSeAMaskGradOp(OpKernelConstruction *context)
+      : OpKernel(context) {
+    OP_REQUIRES_OK(context,
+                   context->GetAttr("total_atom_num", &total_atom_num));
+  }
+
+  void Compute(OpKernelContext *context) override {
+    deepmd::safe_compute(
+        context, [this](OpKernelContext *context) { this->_Compute(context); });
+  }
+
+  void _Compute(OpKernelContext *context) {
+    // Grab the input tensor
+    const Tensor &grad_tensor = context->input(0);
+    const Tensor &net_deriv_tensor = context->input(1);
+    const Tensor &in_deriv_tensor = context->input(2);
+    const Tensor &mask_tensor = context->input(3);
+    const Tensor &nlist_tensor = context->input(4);
+
+    // set size of the sample
+    TensorShape grad_shape = grad_tensor.shape();
+    TensorShape net_deriv_shape = net_deriv_tensor.shape();
+    TensorShape in_deriv_shape = in_deriv_tensor.shape();
+    TensorShape mask_shape = mask_tensor.shape();
+    TensorShape nlist_shape = nlist_tensor.shape();
+
+    OP_REQUIRES(context, (grad_shape.dims() == 2),
+                errors::InvalidArgument("Dim of grad should be 2"));
+    OP_REQUIRES(context, (net_deriv_shape.dims() == 2),
+                errors::InvalidArgument("Dim of net deriv should be 2"));
+    OP_REQUIRES(context, (in_deriv_shape.dims() == 2),
+                errors::InvalidArgument("Dim of input deriv should be 2"));
+    OP_REQUIRES(context, (mask_shape.dims() == 2),
+                errors::InvalidArgument("Dim of mask should be 2"));
+    OP_REQUIRES(context, (nlist_shape.dims() == 2),
+                errors::InvalidArgument("Dim of nlist should be 2"));
+
+    int nframes = net_deriv_tensor.shape().dim_size(0);
+    int nloc = total_atom_num;
+    int ndescrpt = net_deriv_tensor.shape().dim_size(1) / nloc;
+    int nnei = total_atom_num;
+
+    // check the sizes
+    OP_REQUIRES(context, (nframes == grad_shape.dim_size(0)),
+                errors::InvalidArgument("number of frames should match"));
+    OP_REQUIRES(context, (nframes == in_deriv_shape.dim_size(0)),
+                errors::InvalidArgument("number of frames should match"));
+    OP_REQUIRES(context, (nframes == nlist_shape.dim_size(0)),
+                errors::InvalidArgument("number of frames should match"));
+    OP_REQUIRES(context, (nframes == mask_shape.dim_size(0)),
+                errors::InvalidArgument("number of frames should match"));
+
+    OP_REQUIRES(
+        context, (nloc * 3 == grad_shape.dim_size(1)),
+        errors::InvalidArgument("input grad shape should be 3 x natoms"));
+    OP_REQUIRES(context, (nloc * ndescrpt * 3 == in_deriv_shape.dim_size(1)),
+                errors::InvalidArgument("number of descriptors should match"));
+
+    // Create an output tensor
+    TensorShape grad_net_shape;
+    grad_net_shape.AddDim(nframes);
+    grad_net_shape.AddDim(nloc * ndescrpt);
+
+    // allocate the output tensor
+    Tensor *grad_net_tensor = NULL;
+    OP_REQUIRES_OK(
+        context, context->allocate_output(0, grad_net_shape, &grad_net_tensor));
+
+    // flat the tensors
+    auto grad = grad_tensor.flat<FPTYPE>();
+    auto net_deriv = net_deriv_tensor.flat<FPTYPE>();
+    auto in_deriv = in_deriv_tensor.flat<FPTYPE>();
+    auto mask = mask_tensor.flat<int>();
+    auto nlist = nlist_tensor.flat<int>();
+    auto grad_net = grad_net_tensor->flat<FPTYPE>();
+
+    // loop over frames
+#pragma omp parallel for
+    for (int kk = 0; kk < nframes; ++kk) {
+      int grad_iter = kk * nloc * 3;
+      int net_iter = kk * nloc * ndescrpt;
+      int in_iter = kk * nloc * ndescrpt * 3;
+      int nlist_iter = kk * nloc * nnei;
+      int mask_iter = kk * nloc;
+      int grad_net_iter = kk * nloc * ndescrpt;
+
+      // reset the frame to 0
+      for (int ii = 0; ii < nloc; ++ii) {
+        for (int aa = 0; aa < ndescrpt; ++aa) {
+          grad_net(grad_net_iter + ii * ndescrpt + aa) = 0.0;
+        }
+      }
+
+      // compute grad of one frame
+      for (int ii = 0; ii < nloc; ++ii) {
+        int i_idx = ii;
+
+        // deriv wrt center atom
+        for (int aa = 0; aa < ndescrpt; ++aa) {
+          for (int dd = 0; dd < 3; ++dd) {
+            grad_net(grad_net_iter + i_idx * ndescrpt + aa) -=
+                grad(grad_iter + i_idx * 3 + dd) *
+                in_deriv(in_iter + i_idx * ndescrpt * 3 + aa * 3 + dd);
+          }
+        }
+
+        // loop over neighbors
+        for (int jj = 0; jj < nnei; ++jj) {
+          int j_idx = nlist(nlist_iter + i_idx * nnei + jj);
+          // Check if atom j_idx is virtual or if the i_idx is virtual.
+          if (j_idx == i_idx || j_idx < 0) {
+            continue;
+          }
+          /*
+if (j_idx > nloc)
+  j_idx = j_idx % nloc;
+if (j_idx < 0)
+  continue;
+*/
+          int aa_start, aa_end;
+          aa_start = jj * 4;
+          aa_end = jj * 4 + 4;
+          // make_descript_range (aa_start, aa_end, jj);
+          for (int aa = aa_start; aa < aa_end; ++aa) {
+            for (int dd = 0; dd < 3; ++dd) {
+              grad_net(grad_net_iter + i_idx * ndescrpt + aa) +=
+                  grad(grad_iter + j_idx * 3 + dd) *
+                  in_deriv(in_iter + i_idx * ndescrpt * 3 + aa * 3 + dd);
+            }
+          }
+        }
+      }
+    }
+  }
+
+ private:
+  int total_atom_num;
+};
+
+#define REGISTER_CPU(T)                                                       \
+  REGISTER_KERNEL_BUILDER(                                                    \
+      Name("ProdForceSeAMaskGrad").Device(DEVICE_CPU).TypeConstraint<T>("T"), \
+      ProdForceSeAMaskGradOp<CPUDevice, T>);
+REGISTER_CPU(float);
+REGISTER_CPU(double);
diff --git a/source/tests/data_dp_mask/nopbc b/source/tests/data_dp_mask/nopbc
new file mode 100644
index 0000000000..e69de29bb2
diff --git a/source/tests/data_dp_mask/set.000/aparam.npy b/source/tests/data_dp_mask/set.000/aparam.npy
new file mode 100644
index 0000000000..85d2f0800c
Binary files /dev/null and b/source/tests/data_dp_mask/set.000/aparam.npy differ
diff --git a/source/tests/data_dp_mask/set.000/atom_pref.npy b/source/tests/data_dp_mask/set.000/atom_pref.npy
new file mode 100644
index 0000000000..02cca0c60d
Binary files /dev/null and b/source/tests/data_dp_mask/set.000/atom_pref.npy differ
diff --git a/source/tests/data_dp_mask/set.000/box.npy b/source/tests/data_dp_mask/set.000/box.npy
new file mode 100644
index 0000000000..71a7dde5ec
Binary files /dev/null and b/source/tests/data_dp_mask/set.000/box.npy differ
diff --git a/source/tests/data_dp_mask/set.000/coord.npy b/source/tests/data_dp_mask/set.000/coord.npy
new file mode 100644
index 0000000000..f3f86b9622
Binary files /dev/null and b/source/tests/data_dp_mask/set.000/coord.npy differ
diff --git a/source/tests/data_dp_mask/set.000/energy.npy b/source/tests/data_dp_mask/set.000/energy.npy
new file mode 100644
index 0000000000..2861a0836c
Binary files /dev/null and b/source/tests/data_dp_mask/set.000/energy.npy differ
diff --git a/source/tests/data_dp_mask/set.000/force.npy b/source/tests/data_dp_mask/set.000/force.npy
new file mode 100644
index 0000000000..e6536f07ba
Binary files /dev/null and b/source/tests/data_dp_mask/set.000/force.npy differ
diff --git a/source/tests/data_dp_mask/type.raw b/source/tests/data_dp_mask/type.raw
new file mode 100644
index 0000000000..7b829b7f16
--- /dev/null
+++ b/source/tests/data_dp_mask/type.raw
@@ -0,0 +1,147 @@
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diff --git a/source/tests/data_dp_mask/type_map.raw b/source/tests/data_dp_mask/type_map.raw
new file mode 100644
index 0000000000..9b7782b7fb
--- /dev/null
+++ b/source/tests/data_dp_mask/type_map.raw
@@ -0,0 +1,6 @@
+C
+O
+N
+H
+S
+ZN
diff --git a/source/tests/infer/dp4mask.pbtxt b/source/tests/infer/dp4mask.pbtxt
new file mode 100644
index 0000000000..a4a1e46495
--- /dev/null
+++ b/source/tests/infer/dp4mask.pbtxt
@@ -0,0 +1,148543 @@
+node {
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+  op: "Const"
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+    }
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+      }
+    }
+  }
+}
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diff --git a/source/tests/test_descrpt_se_a_mask.py b/source/tests/test_descrpt_se_a_mask.py
new file mode 100644
index 0000000000..131f90fe36
--- /dev/null
+++ b/source/tests/test_descrpt_se_a_mask.py
@@ -0,0 +1,1471 @@
+import os
+import pathlib
+
+import numpy as np
+from common import (
+    Data,
+    DataSystem,
+    gen_data,
+    j_loader,
+)
+from infer.convert2pb import (
+    convert_pbtxt_to_pb,
+)
+
+from deepmd.common import (
+    j_must_have,
+)
+from deepmd.descriptor import (
+    DescrptSeA,
+    DescrptSeAMask,
+)
+from deepmd.env import (
+    tf,
+)
+from deepmd.infer import (
+    DeepPot,
+)
+from deepmd.utils.type_embed import (
+    TypeEmbedNet,
+    embed_atom_type,
+)
+
+GLOBAL_ENER_FLOAT_PRECISION = tf.float64
+GLOBAL_TF_FLOAT_PRECISION = tf.float64
+GLOBAL_NP_FLOAT_PRECISION = np.float64
+
+tests_path = pathlib.Path(__file__).parent.absolute()
+
+
+class TestModel(tf.test.TestCase):
+    @classmethod
+    def setUpClass(cls):
+        convert_pbtxt_to_pb(
+            str(tests_path / os.path.join("infer", "dp4mask.pbtxt")), "dp4mask.pb"
+        )
+        cls.dp = DeepPot("dp4mask.pb")
+
+    def test_dp_mask_model(self):
+        dcoord = np.array(
+            [
+                -6.407,
+                51.239,
+                21.239,
+                -4.533,
+                55.791,
+                24.103,
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+                18.669,
+                -10.607,
+                53.534,
+                20.543,
+                -2.764,
+                53.401,
+                28.036,
+                -11.001,
+                53.126,
+                22.259,
+                -11.154,
+                51.866,
+                20.973,
+                -1.71,
+                54.849,
+                28.274,
+                -3.465,
+                54.929,
+                28.701,
+                0.532,
+                54.416,
+                26.971,
+                1.735,
+                53.526,
+                25.961,
+                1.075,
+                52.76,
+                27.46,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                -3.499,
+                55.357,
+                20.781,
+                -2.882,
+                51.791,
+                21.816,
+                -6.17,
+                52.791,
+                20.442,
+                -4.673,
+                53.978,
+                24.029,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+                -4.296,
+                53.519,
+                21.692,
+            ]
+        )
+        datype = np.array(
+            [
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                1,
+                1,
+                1,
+                1,
+                1,
+                1,
+                1,
+                1,
+                1,
+                1,
+                1,
+                1,
+                1,
+                1,
+                1,
+                1,
+                2,
+                2,
+                2,
+                2,
+                2,
+                2,
+                2,
+                2,
+                2,
+                2,
+                2,
+                2,
+                2,
+                2,
+                2,
+                2,
+                2,
+                2,
+                2,
+                2,
+                2,
+                2,
+                2,
+                2,
+                3,
+                3,
+                3,
+                3,
+                3,
+                3,
+                3,
+                3,
+                3,
+                3,
+                3,
+                3,
+                3,
+                3,
+                3,
+                3,
+                3,
+                3,
+                3,
+                3,
+                3,
+                3,
+                3,
+                3,
+                3,
+                3,
+                3,
+                3,
+                3,
+                3,
+                3,
+                3,
+                3,
+                3,
+                3,
+                3,
+                3,
+                3,
+                3,
+                3,
+                3,
+                3,
+                3,
+                3,
+                3,
+                3,
+                3,
+                3,
+                3,
+                3,
+                3,
+                3,
+                3,
+                3,
+                3,
+                3,
+                3,
+                3,
+                3,
+                3,
+                3,
+                3,
+                3,
+                3,
+                4,
+                4,
+                4,
+                4,
+                4,
+                4,
+                5,
+            ]
+        )
+        aparam = np.array(
+            [
+                1,
+                1,
+                1,
+                1,
+                1,
+                1,
+                1,
+                1,
+                1,
+                1,
+                1,
+                1,
+                1,
+                1,
+                1,
+                1,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                1,
+                1,
+                1,
+                1,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                1,
+                1,
+                1,
+                1,
+                1,
+                1,
+                1,
+                1,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                1,
+                1,
+                1,
+                1,
+                1,
+                1,
+                1,
+                1,
+                1,
+                1,
+                1,
+                1,
+                1,
+                1,
+                1,
+                1,
+                1,
+                1,
+                1,
+                1,
+                1,
+                1,
+                1,
+                1,
+                1,
+                1,
+                1,
+                1,
+                1,
+                1,
+                1,
+                1,
+                1,
+                1,
+                1,
+                1,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                1,
+                1,
+                1,
+                1,
+                0,
+                0,
+                1,
+            ]
+        )
+        dbox = np.array(
+            [20.0, 0, 0, 0, 20.0, 0, 0, 0, 20.0]
+        )  # Not used in parctice. For interface compatibility.
+
+        expected_f = np.array(
+            [
+                -3.5993690e01,
+                -7.7648770e01,
+                1.6714340e01,
+                -2.7043980e01,
+                5.7522240e01,
+                5.0546710e01,
+                4.5166060e01,
+                2.6040450e01,
+                4.8261500e00,
+                1.7129000e00,
+                1.7982240e01,
+                -3.6960410e01,
+                1.5873100e01,
+                -8.4242400e00,
+                -2.5200920e01,
+                -2.0512270e01,
+                -1.2358140e01,
+                3.7627860e01,
+                -9.1338400e00,
+                -4.0187150e01,
+                -2.4780930e01,
+                -2.8910740e01,
+                2.3607110e01,
+                -1.3480000e01,
+                7.0969700e00,
+                -3.7301300e00,
+                -7.6201300e00,
+                -8.7067900e00,
+                -1.4401450e01,
+                6.8929500e00,
+                7.7028100e00,
+                1.4252170e01,
+                7.0598000e00,
+                1.2804130e01,
+                2.7794000e-01,
+                -1.4302700e00,
+                9.0479600e00,
+                -1.6057170e01,
+                2.3842000e-01,
+                -1.0324340e01,
+                -1.5808700e00,
+                1.7572700e00,
+                -5.6691000e-01,
+                -2.6487700e00,
+                1.2565150e01,
+                1.0164590e01,
+                4.1872300e00,
+                7.5286900e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                -8.6003100e00,
+                1.0519000e00,
+                1.0238500e00,
+                1.0853090e01,
+                -5.4747600e00,
+                1.3128300e00,
+                -2.1731100e00,
+                -4.3941000e-01,
+                -1.0032100e01,
+                -8.3830400e00,
+                5.1415500e00,
+                -5.2965000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                3.1024020e01,
+                1.6851350e01,
+                -3.4651860e01,
+                1.0799920e01,
+                2.7493150e01,
+                3.7627860e01,
+                2.9150200e01,
+                -3.6832300e00,
+                1.4268510e01,
+                -1.1658280e01,
+                -5.5203400e00,
+                -2.4266600e00,
+                -2.1513200e01,
+                3.9396740e01,
+                2.2037020e01,
+                1.8250890e01,
+                4.3413000e-01,
+                -1.9913100e00,
+                5.5734400e00,
+                -5.6069800e00,
+                -1.6624750e01,
+                -8.4110300e00,
+                2.3294000e00,
+                -7.0068400e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
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+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                -1.0464110e01,
+                1.0451380e01,
+                4.9436700e00,
+                9.6216800e00,
+                -1.1424330e01,
+                8.1045600e00,
+                -2.2724300e00,
+                -1.4578240e01,
+                -2.7763700e00,
+                9.2650000e-01,
+                -8.4823200e00,
+                1.4528340e01,
+                -9.0125200e00,
+                -5.1504900e00,
+                1.3731300e01,
+                -9.4581000e00,
+                -1.0106400e00,
+                1.4434730e01,
+                1.6992000e00,
+                6.5790400e00,
+                1.7111000e00,
+                -1.1719670e01,
+                3.7697000e00,
+                -2.5802300e00,
+                1.4025330e01,
+                -3.8276400e00,
+                3.2638100e00,
+                2.5671000e-01,
+                -7.5635600e00,
+                -8.3684200e00,
+                -2.2283000e-01,
+                -1.2754010e01,
+                -9.4995800e00,
+                -1.2458010e01,
+                2.1459500e00,
+                4.3690100e00,
+                1.9534400e00,
+                6.4804800e00,
+                1.0346300e01,
+                4.9571900e00,
+                -5.8393700e00,
+                -5.3999900e00,
+                8.4040800e00,
+                1.1162310e01,
+                -7.2808400e00,
+                -3.1794200e00,
+                -8.8637400e00,
+                9.2664000e00,
+                -7.3975500e00,
+                -1.1542260e01,
+                -6.2214300e00,
+                -1.0755400e01,
+                -4.4821800e00,
+                -3.2248400e00,
+                -2.9953900e00,
+                -1.4734280e01,
+                -6.6545400e00,
+                8.4772000e-01,
+                4.0618400e00,
+                -4.1332800e00,
+                2.7551000e-01,
+                4.0179500e00,
+                -7.9780000e-02,
+                2.2621800e00,
+                -3.8397900e00,
+                1.4491500e00,
+                -6.7421000e00,
+                7.2411900e00,
+                2.4156400e00,
+                -6.9857000e00,
+                5.7534200e00,
+                -1.5221540e01,
+                1.3440600e00,
+                -1.5649430e01,
+                -6.0455300e00,
+                -1.4024600e00,
+                -1.3145880e01,
+                5.2747000e-01,
+                -5.4272300e00,
+                1.1973150e01,
+                9.5885400e00,
+                4.3762200e00,
+                -1.1622900e01,
+                1.1301080e01,
+                -1.0030000e-01,
+                1.7600320e01,
+                -4.6429600e00,
+                2.6303800e00,
+                -6.0677900e00,
+                -1.2528040e01,
+                4.0247000e00,
+                1.2156810e01,
+                5.9718100e00,
+                -1.4261530e01,
+                -2.6802700e00,
+                -1.8094600e00,
+                1.1774170e01,
+                -4.7346400e00,
+                -4.9402900e00,
+                2.0064300e00,
+                -1.6625570e01,
+                -7.5587800e00,
+                -1.0956040e01,
+                -2.7341200e00,
+                1.0369560e01,
+                5.4700000e-02,
+                9.6412000e00,
+                -1.1201480e01,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                8.4683690e01,
+                1.5705003e02,
+                -8.6262560e01,
+                1.0821187e02,
+                -1.3312720e02,
+                -1.5838900e00,
+                -2.5402410e01,
+                5.5693000e01,
+                -3.7288700e01,
+                -8.3411400e00,
+                -2.9747100e00,
+                1.4720840e01,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                0.0000000e00,
+                -1.1806986e02,
+                -4.1128690e01,
+                6.9734090e01,
+            ]
+        )
+
+        atom_pref = np.array(
+            [
+                1,
+                1,
+                1,
+                1,
+                1,
+                1,
+                1,
+                1,
+                1,
+                1,
+                1,
+                0,
+                1,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                1,
+                1,
+                1,
+                1,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                1,
+                1,
+                1,
+                0,
+                1,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                1,
+                1,
+                1,
+                1,
+                0,
+                0,
+                1,
+            ]
+        )
+        atom_pref = np.repeat(atom_pref, 3)
+
+        ee, ff, vv = self.dp.eval(dcoord, dbox, datype, aparam=aparam)
+        ff = ff.reshape(expected_f.shape)
+
+        diff_ff = np.multiply(np.square(ff - expected_f), atom_pref)
+        normalized_diff_ff = np.sqrt(np.sum(diff_ff) / np.sum(atom_pref))
+
+        assert normalized_diff_ff < 100
+
+    def test_descriptor_se_a_mask(self):
+        jfile = "zinc_se_a_mask.json"
+        jdata = j_loader(jfile)
+
+        systems = j_must_have(jdata["training"]["validation_data"], "systems")
+        # set_pfx = j_must_have(jdata['validation_data'], "set_prefix")
+        set_pfx = "set"
+        batch_size = 2
+        test_size = 1
+        rcut = 20.0  # For DataSystem interface compatibility, not used in this test.
+        sel = j_must_have(jdata["model"]["descriptor"], "sel")
+        ntypes = len(sel)
+        total_atom_num = np.cumsum(sel)[-1]
+
+        data = DataSystem(systems, set_pfx, batch_size, test_size, rcut, run_opt=None)
+
+        test_data = data.get_test()
+        numb_test = 1
+
+        assert (
+            jdata["model"]["descriptor"]["type"] == "se_a_mask"
+        ), "Wrong descriptor type"
+        descrpt = DescrptSeAMask(**jdata["model"]["descriptor"], uniform_seed=True)
+
+        t_coord = tf.placeholder(
+            GLOBAL_TF_FLOAT_PRECISION, [None, None], name="i_coord"
+        )
+        t_type = tf.placeholder(tf.int32, [None, None], name="i_type")
+        t_natoms = tf.placeholder(tf.int32, [ntypes + 2], name="i_natoms")
+        t_box = tf.placeholder(GLOBAL_TF_FLOAT_PRECISION, [None, 9], name="i_box")
+        t_mesh = tf.placeholder(tf.int32, [None], name="i_mesh")
+        is_training = tf.placeholder(tf.bool)
+        t_aparam = tf.placeholder(tf.int32, [None, None], name="i_aparam")
+
+        dout = descrpt.build(
+            t_coord,
+            t_type,
+            t_natoms,
+            t_box,
+            t_mesh,
+            input_dict={"aparam": t_aparam},
+            reuse=False,
+        )
+
+        # Manually set the aparam to be all zeros. So that all particles are masked as virtual atoms.
+        # This is to test the correctness of the mask.
+        test_data["aparam"] = np.zeros([numb_test, total_atom_num], dtype=np.int32)
+        feed_dict_test = {
+            t_coord: test_data["coord"][:numb_test, :],
+            t_box: test_data["box"][:numb_test, :],
+            t_type: test_data["type"][:numb_test, :],
+            t_natoms: test_data["natoms_vec"],
+            t_mesh: test_data["default_mesh"],
+            t_aparam: test_data["aparam"][:numb_test, :],
+            is_training: False,
+        }
+        sess = self.test_session().__enter__()
+        sess.run(tf.global_variables_initializer())
+        [op_dout] = sess.run([dout], feed_dict=feed_dict_test)
+        op_dout = op_dout.reshape([-1])
+
+        ref_dout = np.zeros(op_dout.shape, dtype=float)
+
+        places = 10
+        np.testing.assert_almost_equal(op_dout, ref_dout, places)
diff --git a/source/tests/zinc_se_a_mask.json b/source/tests/zinc_se_a_mask.json
new file mode 100644
index 0000000000..10094d7301
--- /dev/null
+++ b/source/tests/zinc_se_a_mask.json
@@ -0,0 +1,85 @@
+{
+  "_comment": " model parameters",
+  "model": {
+    "type_map": [
+      "C",
+      "O",
+      "N",
+      "H",
+      "S",
+      "ZN"
+    ],
+    "descriptor": {
+      "type": "se_a_mask",
+      "sel": [
+        36,
+        16,
+        24,
+        64,
+        6,
+        1
+      ],
+      "neuron": [
+        32,
+        32,
+        64,
+        128
+      ],
+      "resnet_dt": true,
+      "axis_neuron": 16,
+      "seed": 1,
+      "_comment": " that's all"
+    },
+    "fitting_net": {
+      "neuron": [
+        240,
+        240,
+        240
+      ],
+      "resnet_dt": true,
+      "seed": 1,
+      "numb_aparam": 1,
+      "use_aparam_as_mask": true,
+      "_comment": " that's all"
+    },
+    "_comment": " that's all"
+  },
+
+  "learning_rate": {
+    "type": "exp",
+    "decay_steps": 20000,
+    "start_lr": 0.001,
+    "stop_lr": 3.51e-8,
+    "_comment": "that's all"
+  },
+
+  "loss": {
+    "type": "ener",
+    "start_pref_e": 0.0,
+    "limit_pref_e": 0.0,
+    "start_pref_f": 0.0,
+    "limit_pref_f": 0.0,
+    "start_pref_pf": 1.0,
+    "limit_pref_pf": 1.0,
+    "_comment": " that's all"
+  },
+  "training": {
+    "validation_data": {
+      "systems": [
+        "source/tests/data_dp_mask/"
+      ],
+      "batch_size": 2,
+      "numb_btch": 1,
+      "_comment": "that's all"
+    },
+    "numb_steps": 1,
+    "seed": 10,
+    "disp_freq": 100,
+    "save_freq": 1000,
+    "tensorboard": true,
+    "tensorboard_log_dir": "log4tensorboard",
+    "tensorboard_freq": 100,
+    "_comment": "that's all"
+  },
+  "_comment": "that's all"
+}