Upcoming Event: Oden Institute Seminar

Neural and spectral operator surrogates

Dr. Jakob Zech, Heidelberg University

Abstract

In this talk we discuss the use of neural network based operator surrogates to approximate smooth maps between infinite-dimensional Hilbert spaces. Such surrogates have a wide range of applications and can be used in uncertainty quantification and parameter estimation problems in fields such as classical mechanics, fluid mechanics, electrodynamics, earth sciences etc. In this case, the operator input represents the problem configuration and models initial conditions, material properties, forcing terms and/or the domain of a partial differential equation (PDE) describing the underlying physics. The output of the operator is the corresponding PDE solution. We will also present an alternative approach using interpolation, which allows for deterministic construction and eliminates the need for training the network weights. In both cases, algebraic and dimension-independent convergence rates are obtained.

 

Biography

I am Juniorprofessor at the Interdisciplinary Center for Scientific Computing at Heidelberg University. Before moving to Heidelberg in April 2020, I was a postdoc at MIT in the group of Youssef Marzouk. In 2018 I completed my PhD at ETH Zürich with Christoph Schwab on Sparse-Grid Approximation of High-Dimensional Parametric PDEs. 

My research focuses on the methodological foundations and theory of forward and inverse problems in Uncertainty Quantification. I am interested in developing and analyzing algorithms for high-dimensional approximation based on sparse-grid techniques, neural networks and transport methods.