The goal of this review paper is to provide the reader with a concise introduction to the
mathematical theory of collision processes in (dilute) gases and plasmas, viewed as a …

The objective of molecular dynamics computations is to infer macroscopic properties of
matter from atomistic models via averages with respect to probability measures dictated by …

Score-based generative models (SGMs) need to approximate the scores $\nabla\log p_t $ of
the intermediate distributions as well as the final distribution $ p_T $ of the forward process …

Multilayer neural networks are among the most powerful models in machine learning, yet the
fundamental reasons for this success defy mathematical understanding. Learning a neural …

The aim of this paper is to introduce a field of study that has emerged over the last decade,
called Bayesian mechanics. Bayesian mechanics is a probabilistic mechanics, comprising …

Classically, the continuous-time Langevin diffusion converges exponentially fast to its
stationary distribution π under the sole assumption that π satisfies a Poincaré inequality …

Solving inverse problems without the use of derivatives or adjoints of the forward model is
highly desirable in many applications arising in science and engineering. In this paper we …

The purpose of this book is to present various results and techniques from the theory of
stochastic processes and in particular diffusion processes that are useful in the study of …

Score-based generative models are shown to achieve remarkable empirical performances
in various applications such as image generation and audio synthesis. However, a …

We study a recently introduced simple method [S. **, N. Liu, and Y. Yu, Quantum simulation
of partial differential equations via Schrödingerisation, arxiv: 2212.13969] for solving …