We present a review of methods for optimal experimental design (OED) for Bayesian inverse
problems governed by partial differential equations with infinite-dimensional parameters …

These lecture notes highlight the mathematical and computational structure relating to the
formulation of, and development of algorithms for, the Bayesian approach to inverse …

Diffusion models have recently emerged as a powerful framework for generative modeling.
They consist of a forward process that perturbs input data with Gaussian white noise and a …

The main objective of this book is to give an overview of the theory of Hamilton–Jacobi–
Bellman (HJB) partial differential equations (PDEs) in infinite-dimensional Hilbert spaces …

Partial differential equations (PDEs) with random input data, such as random loadings and
coefficients, are reformulated as parametric, deterministic PDEs on parameter spaces of …

Since their initial introduction, score-based diffusion models (SDMs) have been successfully
applied to solve a variety of linear inverse problems in finite-dimensional vector spaces due …

This book provides the reader with the principal concepts and results related to differential
properties of measures on infinite dimensional spaces. In the finite dimensional case such …

We study Liouville first passage percolation metrics associated to a Gaussian free field hh
mollified by the two-dimensional heat kernel pt p_t in the bulk, and related star-scale …

We address the problem of optimal experimental design (OED) for Bayesian nonlinear
inverse problems governed by partial differential equations (PDEs). The inverse problem …

We prove the existence of weak solutions to McKean–Vlasov SDEs defined on a domain
D⊆ R d with continuous and unbounded coefficients and degenerate diffusion coefficient …