Related papers: A Full-Density Approach to Simulating Random Itera…

We introduce a finite-volume numerical scheme for solving stochastic gradient-flow equations. Such equations are of crucial importance within the framework of fluctuating hydrodynamics and dynamic density functional theory. Our proposed…

The density ratio of two probability distributions is one of the fundamental tools in mathematical and computational statistics and machine learning, and it has a variety of known applications. Therefore, density ratio estimation from…

Ordinary differential equations (ODEs), via their induced flow maps, provide a powerful framework to parameterize invertible transformations for the purpose of representing complex probability distributions. While such models have achieved…

We present a class of diffusion-based algorithms to draw samples from high-dimensional probability distributions given their unnormalized densities. Ideally, our methods can transport samples from a Gaussian distribution to a specified…

The Regularised Inertial Dean-Kawasaki model (RIDK) -- introduced by the authors and J. Zimmer in earlier works -- is a nonlinear stochastic PDE capturing fluctuations around the mean-field limit for large-scale particle systems in both…

Modeling real-world problems with partial differential equations (PDEs) is a prominent topic in scientific machine learning. Classic solvers for this task continue to play a central role, e.g. to generate training data for deep learning…

The probability density function (PDF) of a random variable associated with the solution of a partial differential equation (PDE) with random parameters is approximated using a truncated series expansion. The random PDE is solved using two…

This paper outlines an approach to the approximation of probability density functions by quadratic forms of weighted orthonormal basis functions with positive semi-definite Hermitian matrices of unit trace. Such matrices are called…

In this paper, we study the finite-horizon optimal density steering problem for discrete-time stochastic linear dynamical systems. Specifically, we focus on steering probability densities represented as Gaussian mixture models which are…

This paper presents a robust version of the stratified sampling method when multiple uncertain input models are considered for stochastic simulation. Various variance reduction techniques have demonstrated their superior performance in…

Density ratio estimation (DRE) is a useful tool for quantifying discrepancies between probability distributions, but existing approaches often involve a trade-off between estimation quality and computational efficiency. Classical direct DRE…

In this article, an overview of Bayesian methods for sequential simulation from posterior distributions of nonlinear and non-Gaussian dynamic systems is presented. The focus is mainly laid on sequential Monte Carlo methods, which are based…

We develop an iterative framework for Bayesian inference problems where the posterior distribution may involve computationally intensive models, intractable gradients, significant posterior concentration, and pronounced non-Gaussianity. Our…

Dynamic Programming (DP) suffers from the well-known ``curse of dimensionality'', further exacerbated by the need to compute expectations over process noise in stochastic models. This paper presents a Monte Carlo-based sampling approach for…

We present new algorithms and fast implementations to find efficient approximations for modelling stochastic processes. For many numerical computations it is essential to develop finite approximations for stochastic processes. While the…

Here we propose the Reweighted Autoencoded Variational Bayes for Enhanced Sampling (RAVE) method, a new iterative scheme that uses the deep learning framework of variational autoencoders to enhance sampling in molecular simulations. RAVE…

An Integral Equation (IE) based field solver to compute the scattered fields from spatially dispersive metasurfaces is proposed and numerically confirmed using various examples involving physical unit cells. The work is a continuation of…

A novel approach called Moate Simulation is presented to provide an accurate numerical evolution of probability distribution functions represented on grids arising from stochastic differential processes where initial conditions are…

In this paper, we consider the composition of two independent processes : one process corresponds to position and the other one to time. Such processes will be called iterated processes. We first propose an algorithm based on the Euler…

Nonparametric tests for equality of multivariate distributions are frequently desired in research. It is commonly required that test-procedures based on relatively small samples of vectors accurately control the corresponding Type I Error…