Seminar by Nicole Aretz

Speaker

Nicole Aretz (The University of Texas at Austin)

Title

Reduced Basis Approximation for Variational Data Assimilation under Model Uncertainty

Date

  • April 25, 2023 16:00 CEST+0200 (Europe/Rome)

  • April 25, 2023 10:00 EDT-0400 (US/Eastern)

  • April 25, 2023 09:00 CDT-0500 (US/Central)

  • April 25, 2023 07:00 PDT-0700 (US/Pacific)

Abstract

Mathematical models, such as partial differential equations (PDEs), are widely used to predict the behavior of a physical system. However, any model can only provide an approximation to the underlying physics, and can be subject to a variety of model errors, such as uncertainties in the loading or initial condition. Variational Data Assimilation can be used to improve models through the incorporation of measurement data. Here, the inverse solution requires many evaluations of the full-order forward model, leading to large computational costs. When the described system configuration is flexible such that the inverse solution needs to be computed for a variety of hyper-parameters, the computational cost becomes prohibitive.

In this talk we present reduced basis (RB) approximations to the 3D-VAR and 4D-VAR variational data assimilation methods posed over hyper-parameterized PDEs with linear model uncertainties. An extension to non-linear inverse problems is shown. After a preparatory offline phase, the RB-3D-VAR and RB-4D-VAR methods can be evaluated at significantly reduced cost, thereby enabling many-query approximations of the inverse solutions for different hyper-parameters and data, while the approximation error can be monitored through rigorous and certified a posteriori error bounds. Focussing on stability theory results, we describe common challenges in these types of RB minimizations, in particular regarding Petrov-Galerkin structures and the role of the adjoint, and discuss tangible approaches for their mitigation. We demonstrate our results on a large-scale geophysical model of the Perth Basin, and on a contaminant-dispersion problem over a Taylor-Green vortex velocity field.

Recording

Watch the recording on our YouTube channel.