The goal is to build a working differentiable wofost72_pp, supporting gradient-based optimization. To make the entire model end-to-end differentiable, the mathematics would be:
$$
\frac{\partial \text{loss}}{\partial \text{(ML model weights)}} =
\frac{\partial \text{loss}}{\partial \text{(differentiable wofost72-pp output)}} \cdot
\frac{\partial \text{(differentiable wofost72-pp output)}}{\partial \text{(wofost72-pp parameters)}} \cdot
\frac{\partial \text{(wofost72-pp parameters)}}{\partial \text{(ML model weights)}}
$$
This approach where an ML model predicts physical parameters, which are then used in a physics-based model, and combines both in a hybrid architecture, is a state-of-the-art approach and is known under various names. See recent publication "Scientific Machine Learning". See similar works at #7 and #13.
The prototype might be:
import torch.nn as nn
# Step 1: ML model that outputs physical parameters e.g. LSTM
class MLModel(nn.Module):
def __init__(self, input_size, hidden_size, num_physical_params):
super().__init__()
self.lstm = nn.LSTM(input_size=input_size, hidden_size=hidden_size, batch_first=True)
self.linear = nn.Linear(hidden_size, num_physical_params)
def forward(self, x):
lstm_out, _ = self.lstm(x)
physical_params = self.linear(lstm_out[:, -1, :])
return physical_params
# Step 2: Physical model using Euler integration
class PhysicalModel(nn.Module):
def __init__(self, dt):
super().__init__()
def forward(self, params):
wofost = Wofost72_PP(params, ...) # this is differentiable version
wofost.run_till_terminate()
output = wofost.get_output()
return output
# Step 3: Hybrid model integrating ML and physical model
class HybridModel(nn.Module):
def __init__(self, input_size, hidden_size, num_physical_params):
super().__init__()
self.ml_model = MLModel(input_size, hidden_size, num_physical_params)
self.physical_model = PhysicalModel()
def forward(self, x):
physical_params = self.ml_model(x)
output = self.physical_model(physical_params)
return output, physical_paramsRegarding this structure, add your comments/suggestions below.
The goal is to build a working differentiable wofost72_pp, supporting gradient-based optimization. To make the entire model end-to-end differentiable, the mathematics would be:
This approach where an ML model predicts physical parameters, which are then used in a physics-based model, and combines both in a hybrid architecture, is a state-of-the-art approach and is known under various names. See recent publication "Scientific Machine Learning". See similar works at #7 and #13.
The prototype might be:
Regarding this structure, add your comments/suggestions below.