5 citations · 10 across the 4 of their papers we have counts for
6 papers · 1 filter
Exponential Convergence of -Time-Stepping in Space-Time Discretizations of Parabolic PDEs
Ilaria Perugia, Christoph Schwab, Marco Zank
For linear parabolic initial-boundary value problems with self-adjoint, time-homogeneous elliptic spatial operator in divergence form with Lipschitz-continuous coefficients, and fo…
Deep ReLU Network Expression Rates for Option Prices in high-dimensional, exponential Lévy models
Lukas Gonon, Christoph Schwab
We study the expression rates of deep neural networks (DNNs for short) for option prices written on baskets of risky assets, whose log-returns are modelled by a multivariate Lé…
Higher-order Quasi-Monte Carlo Training of Deep Neural Networks
M. Longo, S. Mishra, T. K. Rusch +1
We present a novel algorithmic approach and an error analysis leveraging Quasi-Monte Carlo points for training deep neural network (DNN) surrogates of Data-to-Observable (DtO) maps…
Quantized tensor FEM for multiscale problems: diffusion problems in two and three dimensions
V. Kazeev, I. Oseledets, M. Rakhuba +1
Homogenization in terms of multiscale limits transforms a multiscale problem with asymptotically separated microscales posed on a physical domain int…
Tensor Rank bounds for Point Singularities in
Carlo Marcati, Maxim Rakhuba, Christoph Schwab
We analyze rates of approximation by quantized, tensor-structured representations of functions with isolated point singularities in . We consider functions in counta…
Improved Efficiency of a Multi-Index FEM for Computational Uncertainty Quantification
Josef Dick, Michael Feischl, Christoph Schwab
We propose a multi-index algorithm for the Monte Carlo (MC) discretization of a linear, elliptic PDE with affine-parametric input. We prove an error vs. work analysis which allows…