Title: On Invariant-Domain Preserving Uncertainty Quantification for Conservation Laws

Abstract: Conservation or balance laws, partial differential equations for which the evolved state quantities are conserved, model physical phenomena spanning orders of magnitude in spatial and temporal scales. For these problems, numerical and physical complexity mandate intricate schemes to obtain satisfactory capability. Though challenging even in a deterministic setting, as a result of their practical significance, uncertainties permeate these studies: initial conditions, boundary conditions, material characteristics, and equations of state, among other properties and conditions, all contribute sources of uncertainty that preclude mere point estimates in robust, predictive computations. In this talk, we consider invariant-domain preserving uncertainty quantification based on a performant extension of recent advancements in stochastic active discretizations and stochastic finite volume methods for conservation laws. To demonstrate how these advancements enable enhanced propagation of uncertainty, we consider a series of benchmark examples based on Euler's equations.

Biosketch: Dr. Jake J. Harmon is a Scientist in the X Computational Physics Division at Los Alamos National Laboratory (LANL). After completing his PhD in 2022 at Colorado State University, which was supported by the US Department of Defense High Performance Computing and Modernization Program and the US Air Force Research Laboratory, he joined LANL as a postdoc in the Applied Mathematics and Plasma Physics and Center for Nonlinear Studies groups, converting to staff in 2024. His research focuses on numerical methods for multiphysics problems.