1 code implementation • 4 Apr 2023 • Pavol Harar, Lukas Herrmann, Philipp Grohs, David Haselbach
A key shortcoming of these supervised learning methods is their need for large training data sets, typically generated from particle models in conjunction with complex numerical forward models simulating the physics of transmission electron microscopes.
no code implementations • 11 Jul 2022 • Lukas Herrmann, Christoph Schwab, Jakob Zech
Specifically, we study approximation rates for Deep Neural Operator and Generalized Polynomial Chaos (gpc) Operator surrogates for nonlinear, holomorphic maps between infinite-dimensional, separable Hilbert spaces.
no code implementations • 9 Mar 2021 • Philipp Grohs, Lukas Herrmann
The approximation of solutions to second order Hamilton--Jacobi--Bellman (HJB) equations by deep neural networks is investigated.
no code implementations • 10 Jul 2020 • Philipp Grohs, Lukas Herrmann
In recent work it has been established that deep neural networks are capable of approximating solutions to a large class of parabolic partial differential equations without incurring the curse of dimension.