Search Results for author: Lukas Herrmann

Found 4 papers, 1 papers with code

FakET: Simulating Cryo-Electron Tomograms with Neural Style Transfer

1 code implementation4 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.

Data Augmentation Style Transfer

Neural and spectral operator surrogates: unified construction and expression rate bounds

no code implementations11 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.

Deep neural network approximation for high-dimensional parabolic Hamilton-Jacobi-Bellman equations

no code implementations9 Mar 2021 Philipp Grohs, Lukas Herrmann

The approximation of solutions to second order Hamilton--Jacobi--Bellman (HJB) equations by deep neural networks is investigated.

Deep neural network approximation for high-dimensional elliptic PDEs with boundary conditions

no code implementations10 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.

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