Quantum Circuit Encodings of Polynomial Chaos Expansions arXiv preprint, 2025
Junaid Aftab, Christoph Schwab, Haizhao Yang and Jakob Zech Link, BibTex
Sparsity for Infinite-Parametric Holomorphic Functions on Gaussian Spaces arXiv preprint, 2025
Carlo Marcati, Christoph Schwab and Jakob Zech Link, BibTex
Optimal Scheduling of Dynamic Transport arXiv preprint, 2025
Panos Tsimpos, Zhi Ren, Jakob Zech and Youssef Marzouk Link, BibTex
Low Stein Discrepancy via Message-Passing Monte Carlo arXiv preprint, 2025
Nathan Kirk, T. Konstantin Rusch, Jakob Zech and Daniela Rus Link, BibTex
Distribution learning via neural differential equations: minimal energy regularization and approximation theory arXiv preprint, 2025
Youssef Marzouk, Zhi Ren and Jakob Zech Link, BibTex
Statistical Learning Theory for Neural Operators arXiv preprint, 2024
Niklas Reinhardt, Sven Wang and Jakob Zech Link, BibTex
On the mean field limit of consensus based methods arXiv preprint, 2024
Marvin Koß, Simon Weissmann and Jakob Zech Link, BibTex
Mathematical theory of deep learning arXiv preprint, 2024
Philipp Petersen and Jakob Zech Link, BibTex
On the mean-field limit for Stein variational gradient descent: stability and multilevel approximation arXiv preprint, 2024
Simon Weissmann and Jakob Zech Link, BibTex
Books
Analyticity and sparsity in uncertainty quantification for PDEs with Gaussian random field inputs Springer, Cham, 2023
Dinh Dũng, Van Kien Nguyen, Christoph Schwab and Jakob Zech Link, BibTex
Proceedings and Book Chapters
Multilevel Optimization for Inverse Problems PMLR, 2022
Simon Weissmann, Ashia Wilson and Jakob Zech Link, BibTex
Deep learning in high dimension: ReLU neural network expression for Bayesian PDE inversion De Gruyter, Berlin, 2022
Joost A. A. Opschoor, Christoph Schwab and Jakob Zech Link, BibTex
Journal Papers
Metropolis-adjusted interacting particle sampling Statistics and Computing, 2025
Bj\"orn Sprungk, Simon Weissmann and Jakob Zech Link, BibTex
Measure transport via polynomial density surrogates Foundations of Data Science (accepted), 2025
Josephine Westermann and Jakob Zech Link, BibTex
Deep Operator Network Approximation Rates for Lipschitz Operators Analysis and Applications (accepted), 2025
Christoph Schwab, Andreas Stein and Jakob Zech Link, BibTex
Distribution Learning via Neural Differential Equations: A Nonparametric Statistical Perspective Journal of Machine Learning Research, 2024
Youssef Marzouk, Zhi (Robert) Ren, Sven Wang and Jakob Zech Link, BibTex
Neural and spectral operator surrogates: unified construction and expression rate bounds Advances in Computational Mathematics, 2024
Lukas Herrmann, Christoph Schwab and Jakob Zech Link, BibTex
De Rham compatible Deep Neural Network FEM Neural Networks, 2023
Marcello Longo, Joost A.A. Opschoor, Nico Disch, Christoph Schwab and Jakob Zech Link, BibTex
Multilevel domain uncertainty quantification in computational electromagnetics Math. Models Methods Appl. Sci., 2023
Rubén Aylwin, Carlos Jerez-Hanckes, Christoph Schwab and Jakob Zech Link, BibTex
Deep learning in high dimension: neural network expression rates for analytic functions in $L^2(\mathbbR^d,\gamma_d)$ SIAM/ASA J. Uncertain. Quantif., 2023
Christoph Schwab and Jakob Zech Link, BibTex
Sparse approximation of triangular transports, Part II: The infinite-dimensional case Constr. Approx., 2022
Jakob Zech and Youssef Marzouk Link, BibTex
Sparse approximation of triangular transports, Part I: The finite-dimensional case Constr. Approx., 2022
Jakob Zech and Youssef Marzouk Link, BibTex
Exponential ReLU DNN expression of holomorphic maps in high dimension Constr. Approx., 2022
Joost A. A. Opschoor, Christoph Schwab and Jakob Zech Link, BibTex
Deep neural network expression of posterior expectations in Bayesian PDE inversion Inverse Problems, 2020
Lukas Herrmann, Christoph Schwab and Jakob Zech Link, BibTex
Convergence rates of high dimensional Smolyak quadrature ESAIM Math. Model. Numer. Anal., 2020
Jakob Zech and Christoph Schwab Link, BibTex
Domain uncertainty quantification in computational electromagnetics SIAM/ASA J. Uncertain. Quantif., 2020
Ruben Aylwin, Carlos Jerez-Hanckes, Christoph Schwab and Jakob Zech Link, BibTex
Uncertainty quantification for spectral fractional diffusion: sparsity analysis of parametric solutions SIAM/ASA J. Uncertain. Quantif., 2019
Lukas Herrmann, Christoph Schwab and Jakob Zech Link, BibTex
Multilevel approximation of parametric and stochastic PDEs Math. Models Methods Appl. Sci., 2019
Jakob Zech, Dinh Dũng and Christoph Schwab Link, BibTex
Deep learning in high dimension: neural network expression rates for generalized polynomial chaos expansions in UQ Anal. Appl. (Singap.), 2019
Christoph Schwab and Jakob Zech Link, BibTex
Shape holomorphy of the stationary Navier-Stokes equations SIAM J. Math. Anal., 2018
Albert Cohen, Christoph Schwab and Jakob Zech Link, BibTex
Electromagnetic wave scattering by random surfaces: shape holomorphy Math. Models Methods Appl. Sci., 2017
Carlos Jerez-Hanckes, Christoph Schwab and Jakob Zech Link, BibTex
A posteriori error estimation of $hp$-dG finite element methods for highly indefinite Helmholtz problems SIAM J. Numer. Anal., 2015
Stefan Sauter and Jakob Zech Link, BibTex
Theses
Sparse-Grid Approximation of High-Dimensional Parametric PDEs PhD thesis, 2018
Jakob Zech Link, BibTex
A Posteriori Error Estimation of hp-DG Finite Element Methods for Highly Indefinite Helmholtz Problems Master's thesis, 2014
Jakob Zech Link, BibTex