Physics-informed Variational Autoencoders for Improved Robustness to Environmental Factors of Variation

Romain Thoreau, Laurent Risser, Véronique Achard, Béatrice Berthelot, Xavier Briottet

Abstract: The combination of machine learning models with physical models is a recent research path to learn robust data representations. In this paper, we introduce p3VAE, a variational autoencoder that integrates prior physical knowledge about the latent factors of variation that are related to the data acquisition conditions. p3VAE combines standard neural network layers with non-trainable physics layers in order to partially ground the latent space to physical variables. We introduce a semi-supervised learning algorithm that strikes a balance between the machine learning part and the physics part. Experiments on simulated and real data sets demonstrate the benefits of our framework against competing physics-informed and conventional machine learning models, in terms of extrapolation capabilities and interpretability. In particular, we show that p3VAE naturally has interesting disentanglement capabilities. Our code and data have been made publicly available at https://github.com/Romain3Ch216/p3VAE.