The combination of machine learning models with physical models is a recent research path to learn robust data representations. In this paper, we introduce \(\hbox {p}^3\) VAE, a variational autoencoder that integrates prior physical knowledge modeling the generative latent factors of variation that are related to the data acquisition conditions. \(\hbox {p}^3\) VAE combines standard neural network layers with non-trainable physics layers in order to partially ground the latent space to physical variables. In order to fully leverage our physics-informed machine learning model, 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 \(\hbox {p}^3\) VAE naturally has interesting disentanglement capabilities. Our code and data have been made publicly available at https://github.com/Romain3Ch216/p3VAE.
