Surrogate based one-shot formulation for inverse problems and optimization under uncertainty

Simon Weissmann (U Heidelberg)

May 17. 2022, 09:15 — 10:00

We propose a general framework for solving machine learning based optimization problems via one-shot formulation. In particular, we are interested in the application to PDE-constrained optimization under uncertainty and inverse problems. In order to solve these problems typically a large number of PDEs need to be solved. In our approach, we replace the complex forward model by a physics informed surrogate model, e.g. a neural network, which is learned simultaneously when estimating the unknown parameters or solving the optimal control problem. We formulate a penalized empirical risk minimization problem and analyze its consistency in the large sample size limit. Moreover, we develop an algorithmic framework using a penalized stochastic gradient descent method in order to reduce the associated computational costs. This is joint work with Philipp Guth and Claudia Schillings.

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Computational Uncertainty Quantification: Mathematical Foundations, Methodology & Data (Thematic Programme)
Clemens Heitzinger (TU Vienna)
Fabio Nobile (EPFL Lausanne)
Robert Scheichl (U Heidelberg)
Christoph Schwab (ETH Zürich)
Sara van de Geer (ETH Zürich)
Karen Willcox (U of Texas, Austin)