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.

翻译：将机器学习模型与物理模型相结合是近期探索鲁棒数据表示的研究路径。本文提出p$^3$VAE，一种融合了完美物理模型的生成模型，该物理模型能部分解释数据中真实潜在变化因素。为充分利用混合架构优势，我们提出半监督优化流程及带有有意义不确定性估计的推理方案。我们将p$^3$VAE应用于高分辨率高光谱遥感图像的语义分割。在模拟数据集上的实验表明，与传统机器学习模型相比，混合模型在外推能力和可解释性方面具有显著优势，特别是展示了p$^3$VAE天然具备的高解耦能力。我们的代码与数据已在https://github.com/Romain3Ch216/p3VAE 公开。