6 papers
Operator Surrogates
Christoph Schwab, Josephine Westermann, Jakob Zech
This chapter provides a mathematical introduction to operator surrogates, which are finite-parametric maps approximating complex (typically nonlinear) operators between infinite-di…
Neural and Spectral Operator Surrogates on Gaussian Spaces
Carlo Marcati, Mario Marić, Christoph Schwab +1
We prove expression rate bounds of finite-parametric, spectral and neural surrogates for holomorphic maps between separable Hilbert spaces. The surrogates have an encoder-approxima…
Approximation of PDE solution manifolds: Sparse-grid interpolation and quadrature
Dinh Dũng, Van Kien Nguyen, Duong Thanh Pham +1
We study fully-discrete approximations and quadratures of infinite-variate functions in abstract Bochner spaces associated with a Hilbert space and an infinite-tensor-product J…
Quantum Circuit Encodings of Polynomial Chaos Expansions
Junaid Aftab, Christoph Schwab, Haizhao Yang +1
This work investigates the expressive power of quantum circuits in approximating high-dimensional, real-valued functions. We focus on countably-parametric holomorphic maps $u:U\to…
Sparsity for Infinite-Parametric Holomorphic Functions on Gaussian Spaces
Carlo Marcati, Christoph Schwab, Jakob Zech
We investigate the sparsity of Wiener polynomial chaos expansions of holomorphic maps on Gaussian Hilbert spaces, as arise in the coefficient-to-solution maps of line…
Frequency-Explicit Shape Holomorphy in Uncertainty Quantification for Acoustic Scattering
Ralf Hiptmair, Christoph Schwab, Euan A. Spence
We consider frequency-domain acoustic scattering at a homogeneous star-shaped penetrable obstacle, whose shape is uncertain and modelled via a radial spectral parameterization with…