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 variational autoencoder that integrates prior physical knowledge about the latent factors of variation that are related to the data acquisition conditions. p$^3$VAE combines standard neural network layers with non-trainable physics layers in order to partially ground the latent space to physical variables. 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 p$^3$VAE naturally has interesting 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学习鲁棒数据表示的新兴研究方向。本文提出p$^3$VAE——一种融合了关于数据采集条件相关潜在变化因素先验物理知识的变分自编码器。p$^3$VAE通过将标准神经网络层与不可训练的物理层相结合，实现潜在空间与物理变量的部分关联。我们提出一种半监督学习算法，在机器学习部分与物理部分之间建立平衡。在仿真和真实数据集上的实验表明，相较于其他物理信息模型和传统机器学习模型，我们的框架在外推能力和可解释性方面具有优势。特别地，我们证明p$^3$VAE天然具备优异的解耦能力。我们的代码与数据已公开于https://github.com/Romain3Ch216/p3VAE。