Quantifying the uncertainty of supervised learning models plays an important role in making
more reliable predictions. Epistemic uncertainty, which usually is due to insufficient …

Questions of 'how best to acquire data'are essential to modelling and prediction in the
natural and social sciences, engineering applications, and beyond. Optimal experimental …

This article addresses the inference of physics models from data, from the perspectives of
inverse problems and model reduction. These fields develop formulations that integrate data …

Mathematics in Zurich has a long and distinguished tradition, in which the writing of lecture
notes volumes and research monographs plays a prominent part. The Zurich Lectures in …

Uncertainty Quantification (UQ) is an emerging and extremely active research discipline
which aims to quantitatively treat any uncertainty in applied models. The primary objective of …

We explore using neural operators, or neural network representations of nonlinear maps
between function spaces, to accelerate infinite-dimensional Bayesian inverse problems …

We propose a dimension reduction technique for Bayesian inverse problems with nonlinear
forward operators, non-Gaussian priors, and non-Gaussian observation noise. The …

This paper aims at revisiting the classical results on Laplace approximation in a modern
nonasymptotic and dimension-free form. Such an extension is motivated by applications to …

The fundamental computational issues in Bayesian inverse problems (BIPs) governed by
partial differential equations (PDEs) stem from the requirement of repeated forward model …

Importance sampling (IS) is valuable in reducing the variance of Monte Carlo sampling for
many areas, including finance, rare event simulation, and Bayesian inference. It is natural …