p$^3$VAE: a physics-integrated generative model. Application to the semantic segmentation of optical remote sensing images

The combination of machine learning models with physical models is a recent research path to learn robust data representations. In this paper, we introduce p$^3$VAE, a generative model that integrates a perfect physical model which partially explains the true underlying factors of variation in the data. To fully leverage our hybrid design, we propose a semi-supervised optimization procedure and an inference scheme that comes along meaningful uncertainty estimates. We apply p$^3$VAE to the semantic segmentation of high-resolution hyperspectral remote sensing images. Our experiments on a simulated data set demonstrated the benefits of our hybrid model against conventional machine learning models in terms of extrapolation capabilities and interpretability. In particular, we show that p$^3$VAE naturally has high disentanglement capabilities. Our code and data have been made publicly available at https://github.com/Romain3Ch216/p3VAE.