Publications

Preprints

  • 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
    Ch. Schwab and J. Zech
    link

Journal papers, conference papers and book chapters

  • Multilevel Optimization for Inverse Problems
    COLT 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