Physics-Integrated Variational Autoencoders for Robust and Interpretable Generative Modeling

Integrating physics models within machine learning models holds considerable\npromise toward learning robust models with improved interpretability and\nabilities to extrapolate. In this work, we focus on the integration of\nincomplete physics models into deep generative models. In particular, we\nintroduce an architecture of variational autoencoders (VAEs) in which a part of\nthe latent space is grounded by physics. A key technical challenge is to strike\na balance between the incomplete physics and trainable components such as\nneural networks for ensuring that the physics part is used in a meaningful\nmanner. To this end, we propose a regularized learning method that controls the\neffect of the trainable components and preserves the semantics of the\nphysics-based latent variables as intended. We not only demonstrate generative\nperformance improvements over a set of synthetic and real-world datasets, but\nwe also show that we learn robust models that can consistently extrapolate\nbeyond the training distribution in a meaningful manner. Moreover, we show that\nwe can control the generative process in an interpretable manner.\n