A NewtonianVAE learns a linear latent dynamic model from high dimensional data, such that proportionality holds in the latent space. The notebook Pointmass_demo provides a minimum working example of a Newtonian VAE trained on images of a point mass, along with latent space visualisation during training.
NewtonianVAE: Proportional Control and Goal Identification From Pixels via Physical Latent Spaces. Miguel Jaques, Michael Burke, Timothy M. Hospedales; Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2021, pp. 4454-4463 [pdf] [arXiv]