Colloquium: Dr. Hans-Werner van Wyk, Department of Scientific Computing, Florida State University

Dr. Hans-Werner van Wyk, Department of Scientific Computing, Florida State University

Title: Modeling, Simulation, and Design of Distributed Parameter Systems under Uncertainty

Abstract: While physical systems involving sound, heat, electrostatics, electrodynamics, fluid flow, or elasticity are generally modeled and understood in the deterministic language of partial differential equations, they often operate within complex environments that cannot be described, or even observed directly, in full deterministic detail. As simulation plays an increasingly central role in modern science and engineering research, by supplementing experiments, aiding in the prototyping of engineering systems or informing decisions on safety and reliability, the need to quantify uncertainty in model outputs due to uncertainties in the model parameters becomes critical. In this talk, we discuss some of the mathematical and computational challenges of uncertainty quantification for distributed parameter systems, and present our contributions to this field. These include: 1) the statistical identification of spatially varying model parameters from measurements of related observable quantities, 2) the numerical simulation of scale-invariant noisefields over arbitrary spatial regions and on general grids, 3) the development of multilevel sampling methods to improve the efficiency of stochastic simulations through the dynamic incorporation of the model's numerical discretization, and 4) an examination of the interplay between parameter uncertainty and model sensitivity.

Faculty host: Yanzhao Cao