Publications

Preprints

  • 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
    Technical report 2020-02, Seminar for Applied Mathematics, ETH Zürich, 2020
    L. Herrmann, Ch. Schwab and J. Zech
    link
  • Exponential ReLU DNN expression of holomorphic maps in high dimension
    Technical report 2019-35, Seminar for Applied Mathematics, ETH Zürich, 2019
    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