  Integrating physics models within machine learning holds considerable promise
toward learning robust models with improved interpretability and abilities to
extrapolate. In this work, we focus on the integration of incomplete physics
models into deep generative models, variational autoencoders (VAEs) in
particular. A key technical challenge is to strike a balance between the
incomplete physics model and the learned components (i.e., neural nets) of the
complete model, in order to ensure that the physics part is used in a
meaningful manner. To this end, we propose a VAE architecture in which a part
of the latent space is grounded by physics. We couple it with a set of
regularizers that control the effect of the learned components and preserve the
semantics of the physics-based latent variables as intended. We not only
demonstrate generative performance improvements over a set of synthetic and
real-world datasets, but we also show that we learn robust models that can
consistently extrapolate beyond the training distribution in a meaningful
manner. Moreover, we show that we can control the generative process in an
interpretable manner.
