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 physical model which deterministically models some of the true underlying factors of variation in the data. To fully leverage our hybrid design, we enhance an existing semi-supervised optimization technique and introduce a new inference scheme that comes along meaningful uncertainty estimates. We apply p$^3$VAE to the pixel-wise classification of airborne hyperspectral images. Our experiments on simulated and real data demonstrate 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.

翻译：将机器学习模型与物理模型相结合是近期学习鲁棒数据表示的研究路径。本文提出p$^3$VAE，这是一种整合了物理模型的生成模型，该物理模型可确定性建模数据中部分真实潜在变化因素。为充分挖掘混合设计的潜力，我们改进了现有半监督优化技术，并引入了一种伴随有意义不确定性估计的新型推理方案。我们将p$^3$VAE应用于机载高光谱图像的逐像素分类。在模拟与真实数据上的实验表明，相较于传统机器学习模型，我们的混合模型在外推能力与可解释性方面具有显著优势。特别地，我们证明了p$^3$VAE天然具备卓越的解耦能力。相关代码与数据已公开发布于https://github.com/Romain3Ch216/p3VAE。