Neural Operators for Elliptic PDEs in Polytopes and Operator Networks via Fixed Point Iterations

27 Mar 2026 03.30 PM - 04.30 PM SPMS-LT5 (SPMS-03-08) Current Students

Abstract
We review recent results and ongoing research on numerical analysis of neural operators, in the references below.
References:

  • Neural General Operator Networks via Banach Fixed Point Iterations M Feischl, Ch Schwab, F Zehetgruber Research Report 2025-13, SAM, ETH Zurich, April 2025 (to appear 2026)

    https://math.ethz.ch/sam/research/reports.html?id=1134

  • Neural and spectral operator surrogates: construction and expression rate bounds L Herrmann, Ch Schwab, J Zech Advances in Computational Mathematics 50 (4), 72, 2024

  • Exponential convergence of deep operator networks for elliptic partial differential equations C Marcati, Ch Schwab SIAM Journal on Numerical Analysis 61 (3), 1513-1545, 2024

  • Expression Rates of Neural Operators for Linear Elliptic PDEs in Polytopes C Marcati, C Schwab arXiv preprint arXiv:2409.17552 =


Biography
Professor Christoph Schwab is a leading expert in numerical analysis and scientific computing. His research interests include space-​time compressive discretisations of evolution equations, PDEs with random input data, high-​​dimensional numerics for PDEs with multiple scales, sparse tensor approximations of high-​​dimensional and stochastic PDEs, multilevel Monte ​Carlo and Quasi-​​Monte Carlo algorithms for PDEs, deep neural network approximation.

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