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Physics-informed Machine Learning for Inverse Problems
Abstract
The problem of learning a generative model governing the dynamics of a physical system appears in many areas of science and engineering. In addition to enabling novel strategies for planning and control, the learned generative model can also be leveraged for forecasting, condition monitoring, and system optimization. However, to tackle the non-uniqueness of solutions and achieve generalization beyond the training dataset, solution approaches to these inverse problems must incorporate appropriate inductive bias, which, for neural networks, can originate from its computation graph or the use of regularization term in the loss function. This talk will focus on learning a generative model from data and demonstrate the effectiveness of using a physics-informed inductive bias in such problems. In particular, we will introduce a learning framework that enforces energy conservation by encoding Hamiltonian dynamics into its computation graph. We will show that the use of physics-informed inductive bias improves prediction accuracy, generalization performance, sample efficiency, and model interpretability.