When
Where
Student: Teddy Meissner, Program in Applied Mathematics
Title: Hybrid State and Parameter Estimation for Model Discovery, and Physics-Informed Forward Simulation
Advisors: Dr. Karl Glasner, Department of Mathematics
Location: MATH 402, Zoom link: https://arizona.zoom.us/j/86857824693
Abstract: Differential equations govern most physical systems, yet in real-world settings two challenges persist, and likely always will: many governing models are unknown or only approximately known, and even known models can only be solved approximately, since exact solutions are rarely available. This defense takes steps addressing both challenges, along with the failure modes each approach runs into and the open directions they point toward. For unknown models, we develop a data-assimilation-based approach to symbolic model discovery, recovering analytical governing equations from data in a way that is robust to high levels of noise, and show that exploiting the underlying model discretization makes the resulting large-scale nonlinear optimization tractable. For forward simulation, physics-informed neural networks offer a promising alternative to costly classical solvers, but their accuracy is often held back by empirical, hand-tuned weightings in their loss functions. We address this by combining physics-informed neural networks with classical elliptic regularity theory, replacing these empirical weightings with theoretically grounded norms, which is shown to greatly improve accuracy on Stokes and Navier-Stokes test cases. We close by outlining directions for extending both approaches beyond the settings considered here.