DMS Colloquium: Hans-Werner van Wyk

Speaker: Hans-Werner van Wyk

Title: The Propagation of Uncertainty through Differential Equations

Abstract: Many complex physical processes can be adequately described in the deterministic language of partial differential equations (PDEs), yet operate in uncertain environments that can only be observed partially and/or indirectly. This aleatory uncertainty manifests itself in the underlying system parameters. My work centers on its identification and propagation through to quantities of interest related to the system's output. This talk highlights my contributions in this area, particularly in improving the efficiency of sampling methods by exploiting multiscale features of random inputs, by designing quadrature schemes tailored to the underlying density, or through the use of reduced order models. I will also discuss some applications of my work, ranging from the prediction of saltwater intrusion, to the development of reliable spectral diagnostics for astrophysical plasmas.