We present a general kernel-based framework for learning operators between Banach
spaces along with a priori error analysis and comprehensive numerical comparisons with …

The quantification of probabilistic uncertainties in the outputs of physical, biological, and
social systems governed by partial differential equations with random inputs require, in …

Parametrized families of PDEs arise in various contexts such as inverse problems, control
and optimization, risk assessment, and uncertainty quantification. In most of these …

We consider the problem of Lagrange polynomial interpolation in high or countably infinite
dimension, motivated by the fast computation of solutions to partial differential equations …

Learning approximations to smooth target functions of many variables from finite sets of
pointwise samples is an important task in scientific computing and its many applications in …

In this paper we present a basis selection method that can be used with ℓ 1-minimization to
adaptively determine the large coefficients of polynomial chaos expansions (PCE). The …

Deep learning (DL) is transforming whole industries as complicated decision-making
processes are being automated by deep neural networks (DNNs) trained on real-world data …

This work proposes a method for sparse polynomial chaos (PC) approximation of high-
dimensional stochastic functions based on non-adapted random sampling. We modify the …

Hierarchical tensors can be regarded as a generalisation, preserving many crucial features,
of the singular value decomposition to higher-order tensors. For a given tensor product …

Shannon-type expected information gain can be used to evaluate the relevance of a
proposed experiment subjected to uncertainty. The estimation of such gain, however, relies …