Neural and gpc operator surrogates: construction and expression rate bounds
preprint, 2022
L. Herrmann, Ch. Schwab and J. Zech link
De Rham compatible Deep Neural Networks
arXiv preprint, 2022
M. Longo, J. A. A. Opschoor, N. Disch, Ch. Schwab and J. Zech link
Analyticity and sparsity in uncertainty quantification for PDEs with Gaussian random field inputs
arXiv preprint, 2022
Dinh Dũng, Van Kien Nguyen, Christoph Schwab and Jakob Zech link
Deep Learning in High Dimension: Neural Network Approximation of Analytic Functions in L2 w.r.t. Gaussian measures
arXiv preprint, 2021 (accepted in JUQ)
Ch. Schwab and J. Zech link
Journal papers, conference papers and book chapters
Multilevel Optimization for Inverse Problems
Proceedings of Machine Learning Research, Volume 178: Conference on Learning Theory, 2022
S. Weissmann, A. Wilson and J. Zech link
Sparse Approximation of Triangular Transports, Part II: The Infinite-Dimensional Case Constructive Approximation, 2022
J. Zech and Y. Marzouk link
Sparse Approximation of Triangular Transports, Part I: The Finite-Dimensional Case Constructive Approximation, 2022
J. Zech and Y. Marzouk link
Deep learning in high dimension: ReLU neural network expression for Bayesian PDE inversion Optimization and Control for Partial Differential Equations: Uncertainty quantification, open and closed-loop control, and shape optimization,
De Gruyter, 419-462, 2022
J. A. A. Opschoor, Ch. Schwab and J. Zech link
Exponential ReLU DNN expression of holomorphic maps in high dimension Constructive Approximation, 2021
J. A. A. Opschoor, Ch. Schwab and J. Zech link
Deep neural network expression of posterior expectations in Bayesian PDE inversion Inverse Problems, Vol. 36, No. 12, 2020
L. Herrmann, Ch. Schwab and J. Zech link
Convergence rates of high dimensional Smolyak quadrature Mathematical Modelling and Numerical Analysis,
Vol. 54, No. 4, 1259 - 1307, 2020
J. Zech and Ch. Schwab link
Domain Uncertainty Quantification in Computational Electromagnetics SIAM/ASA J. Uncertain. Quantif., Vol. 8, No. 1, 301-341, 2020
R. Aylwin, C. Jerez-Hanckes, Ch. Schwab and J. Zech link
Uncertainty Quantification for Spectral Fractional Diffusion: Sparsity Analysis of Parametric Solutions SIAM/ASA J. Uncertain. Quantif., Vol. 7, No. 3, 913-947, 2019
L. Herrmann, Ch. Schwab and J. Zech link
Multilevel approximation of parametric and stochastic PDEs Math. Models Methods Appl. Sci., Vol. 29, No. 9, 1753-1817, 2019
J. Zech, D. Dung and Ch. Schwab link
Deep learning in high dimension: neural network expression rates for generalized polynomial chaos expansions in UQ Analysis and Applications, Vol. 17, No. 1, pp. 19-55, 2019
Ch. Schwab and J. Zech link
Shape Holomorphy of the Stationary Navier-Stokes Equations SIAM Journal on Mathematical Analysis , Vol. 50, No. 2, pp. 1720-1752, 2018
A. Cohen, Ch. Schwab and J. Zech link
Electromagnetic wave scattering by random surfaces: Shape holomorphy Mathematical Models and Methods in Applied Sciences Vol. 27, No. 12, pp. 2229-2259, 2017
C. Jerez-Hanckes, Ch. Schwab and J. Zech link
A posteriori error estimation of hp-dG finite element methods for highly indefinite Helmholtz problems SIAM Journal on Numerical Analysis Vol. 53, No. 5, pp. 2414-2440, 2015
S. Sauter and J. Zech link
Theses
Sparse-Grid Approximation of High-Dimensional Parametric PDEs
PhD thesis, Advisor: Prof. Dr. Christoph Schwab, ETH Zürich, 2018
J. Zech link
A Posteriori Error Estimation of hp-DG Finite Element Methods for Highly IndefiniteHelmholtz Problems
Master's thesis, Advisor: Prof. Dr. Stefan Sauter, ETH Zürich and Universität Zürich, 2014
J. Zech link