Publications

Preprints

  • On the mean-field limit for Stein variational gradient descent: stability and multilevel approximation
    arXiv preprint, 2024
    S. Weissmann, J. Zech
    link
  • Metropolis-adjusted interacting particle sampling
    arXiv preprint, 2023
    B. Sprungk, S. Weissmann, J. Zech
    link
  • Measure transport via polynomial density surrogates
    arXiv preprint, 2023
    J. Westermann and J. Zech
    link
  • Distribution learning via neural differential equations: a nonparametric statistical perspective
    arXiv preprint, 2023
    Y. Marzouk, Z. Ren, S. Wang, J. Zech
    link
  • Deep Operator Network Approximation Rates for Lipschitz Operators
    arXiv preprint, 2023
    A. Stein, Ch. Schwab and J. Zech
    link
  • Neural and spectral operator surrogates: unified construction and expression rate bounds
    arXiv preprint, 2022
    L. Herrmann, Ch. Schwab and J. Zech
    link

Books

  • Analyticity and sparsity in uncertainty quantification for PDEs with Gaussian random field inputs
    Springer Lecture Notes in Mathematics, 2023
    Dinh Dũng, Van Kien Nguyen, Christoph Schwab and Jakob Zech
    link

Proceedings 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
  • 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

Journal papers

  • De Rham compatible Deep Neural Network FEM
    Neural Networks, 2023
    M. Longo, J. A. A. Opschoor, N. Disch, Ch. Schwab and J. Zech
    link
  • Multilevel Domain Uncertainty Quantification in Computational Electromagnetics
    Mathematical Models and Methods in Applied Sciences, 2023
    R. Aylwin, C. Jerez-Hanckes, Ch. Schwab and J. Zech
    link
  • Deep Learning in High Dimension: Neural Network Approximation of Analytic Functions in L2 w.r.t. Gaussian measures
    SIAM/ASA Journal of Uncertainty Quantification, 2022
    Ch. Schwab 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
  • 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