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The combination of machine learning models with physical models is a recentresearch path to learn robust data representations. In this paper, we introducep$^3$VAE, a variational autoencoder that integrates prior physical knowledgeabout the latent factors of variation that are related to the data acquisitionconditions. p$^3$VAE combines standard neural network layers with non-trainablephysics layers in order to partially ground the latent space to physicalvariables. We introduce a semi-supervised learning algorithm that strikes abalance between the machine learning part and the physics part. Experiments onsimulated and real data sets demonstrate the benefits of our framework againstcompeting physics-informed and conventional machine learning models, in termsof extrapolation capabilities and interpretability. In particular, we show thatp$^3$VAE naturally has interesting disentanglement capabilities. Our code anddata have been made publicly available athttps://github.com/Romain3Ch216/p3VAE.

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