Publications

Preprints

  • On the mean-field limit for Stein variational gradient descent: stability and multilevel approximation
    arXiv preprint, 2024
    Simon Weissmann and Jakob Zech
    Link, BibTex
  • Metropolis-adjusted interacting particle sampling
    arXiv preprint, 2023
    Björn Sprungk, Simon Weissmann and Jakob Zech
    Link, BibTex
  • Measure transport via polynomial density surrogates
    arXiv preprint, 2023
    Josephine Westermann and Jakob Zech
    Link, BibTex
  • Distribution learning via neural differential equations: a nonparametric statistical perspective
    arXiv preprint, 2023
    Youssef Marzouk, Zhi Ren, Sven Wang and Jakob Zech
    Link, BibTex
  • Deep Operator Network Approximation Rates for Lipschitz Operators
    arXiv preprint, 2023
    Christoph Schwab, Andreas Stein and Jakob Zech
    Link, BibTex
  • Neural and spectral operator surrogates: unified construction and expression rate bounds
    arXiv preprint, 2022
    Lukas Herrmann, Christoph Schwab 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

  • 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