(416i) Machine Learning with Differential Equation Priors

Modeling the differential equations governing physical systems is a central aspect of many science and engineering tasks. These systems verify exact constraints corresponding to the laws of physics. Recently, neural network approaches have shown promise in solving differential equations via approximating functions. However, these approaches only approximately enforce the constraints on a physical system. I will first discuss the challenges associated with such an approach. I will then discuss overcoming these challenges by developing a neural network architecture that incorporates differential equation constrained optimization, which outputs solutions that verify the desired physical constraints exactly over a given spatial and/or temporal domain. I will show that this architecture allows us to accurately and efficiently fit solutions to new problems, and demonstrate this on fluid flow and transport phenomena problems.