Physics-guided machine learning from simulated data with different physical parameters

Physics-based models are widely used to study dynamical systems in a variety of scientific and engineering problems. However, these models are necessarily approximations of reality due to incomplete knowledge or excessive complexity in modeling underlying processes. As a result, they often produce biased simulations due to inaccurate parameterizations or approximations used to represent the true physics. In this paper, we aim to build a new physics-guided machine learning framework to monitor dynamical systems. The idea is to use advanced machine learning model to extract complex spatio-temporal data patterns while also incorporating general scientific knowledge embodied in simulated data generated by the physics-based model. To handle the bias in simulated data caused by imperfect parameterization, we propose to extract general physical relations jointly from multiple sets of simulations generated by a physics-based model under different physical parameters. In particular, we develop a spatio-temporal network architecture that uses its gating variables to capture the variation of physical parameters. We initialize this model using a pre-training strategy that helps discover common physical patterns shared by different sets of simulated data. Then, we fine-tune it combining limited observations and adequate simulations. By leveraging the complementary strength of machine learning and domain knowledge, our method has been shown to produce accurate predictions, use less training samples and generalize to out-of-sample scenarios. We further show that the method can provide insights about the variation of physical parameters over space and time in two domain applications: predicting temperature in streams and predicting temperature in lakes.