In this survey, we describe controlled interacting particle systems (CIPS) to approximate the
solution of the optimal filtering and the optimal control problems. Part I of the survey is …

Bayesian inference problems require sampling or approximating high-dimensional
probability distributions. The focus of this paper is on the recently introduced Stein …

While Bayesian neural networks (BNNs) have drawn increasing attention, their posterior
inference remains challenging, due to the high-dimensional and over-parameterized nature …

We present a framework for Nesterov's accelerated gradient flows in probability space to
design efficient mean-field Markov chain Monte Carlo algorithms for Bayesian inverse …

We introduce a framework for Newton's flows in probability space with information metrics,
named information Newton's flows. Here two information metrics are considered, including …

This paper presents a methodology and numerical algorithms for constructing accelerated
gradient flows on the space of probability distributions. In particular, we extend the recent …

The article considers smooth optimization of functions on Lie groups. By generalizing NAG
variational principle in vector space (Wibisono et al., 2016) to general Lie groups …

It is known that the Langevin dynamics used in MCMC is the gradient flow of the KL
divergence on the Wasserstein space, which helps convergence analysis and inspires …

The Straight-Through (ST) estimator is a widely used technique for back-propagating
gradients through discrete random variables. However, this effective method lacks …

Model Updating is frequently used in Structural Health Monitoring to determine structures'
operating conditions and whether maintenance is required. Data collected by sensors are …