Physics-informed and Equality-constrained Artificial Neural Networks with Applications to Partial Differential Equations and Multi-fidelity Data Assimilation

Understanding the complexity of the physical universe in its details is a challenging endeavor. However, many physical processes integral to engineering applications can be concisely described by a set of unified governing laws. In this study, we investigate the application of artificial neural networks to mining physics. Particularly, we discuss the challenges associated with integrating observational data with known laws of physics. We then present a neural network-based approach that recasts solving a phenomena governed by known physics as a constrained optimization problem. Our approach is noise-aware, physics-informed, equality-constrained and adept at multi-fidelity data fusion. We demonstrate the efficacy and versatility of our approach by applying it to the solution of several challenging problems governed by linear and non-linear partial differential equations.