Deep learning in high dimension: ReLU network Expression Rates for Bayesian PDE inversion
Technical report 2020-47, Seminar for Applied Mathematics, ETH Zürich, 2020
J. A. A. Opschoor, Ch. Schwab and J. Zech link
Sparse approximation of triangular transports on bounded domains
Technical report, 2020
J. Zech and Y. Marzouk link
Deep ReLU Neural Network Expression Rates for Data-to-QoI Maps in Bayesian PDE Inversion
to appear in Inverse Problems
L. Herrmann, Ch. Schwab and J. Zech link
Exponential ReLU DNN expression of holomorphic maps in high dimension
to appear in Constructive Approximation
J. A. A. Opschoor, Ch. Schwab and J. Zech link
Journal Papers
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