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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 generative model that integrates a physical model whichdeterministically models some of the true underlying factors of variation inthe data. To fully leverage our hybrid design, we enhance an existingsemi-supervised optimization technique and introduce a new inference schemethat comes along meaningful uncertainty estimates. We apply p$^3$VAE to thepixel-wise classification of airborne hyperspectral images. Our experiments onsimulated and real data demonstrate the benefits of our hybrid model againstconventional machine learning models in terms of extrapolation capabilities andinterpretability. In particular, we show that p$^3$VAE naturally has highdisentanglement capabilities. Our code and data have been made publiclyavailable at https://github.com/Romain3Ch216/p3VAE.

p$^3$VAE: a physics-integrated generative model. Application to the pixel-wise classification of airborne hyperspectral images