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Mathematically modelling diffusive and advective transport of particles in heterogeneous layered media is important to many applications in computational, biological and medical physics. While deterministic continuum models of such…
A new approach for the analysis of Langevin-type stochastic processes in the presence of strong measurement noise is presented. For the case of Gaussian distributed, exponentially correlated, measurement noise it is possible to extract the…
Recovering a stochastic process from noisy ensembles of single particle trajectories (SPTs) is resolved here using the Langevin equation as a model. The massive redundancy contained in SPTs data allows recovering local parameters of the…
The likelihood functions for discretely observed nonlinear continuous-time models based on stochastic differential equations are not available except for a few cases. Various parameter estimation techniques have been proposed, each with…
In this paper, we study the problem of computing the effective diffusivity for particles moving in chaotic flows. Instead of solving a convection-diffusion type cell problem in the Eulerian formulation (arising from homogenization theory…
Stochastic variational integrators for constrained, stochastic mechanical systems are developed in this paper. The main results of the paper are twofold: an equivalence is established between a stochastic Hamilton-Pontryagin (HP) principle…
This letter deals with the problem of state estimation for a class of systems involving linear dynamics with multiple quadratic output measurements. We propose a systematic approach to immerse the original system into a linear time-varying…
In this paper, we develop variational integrators for the nonequilibrium thermodynamics of simple closed systems. These integrators are obtained by a discretization of the Lagrangian variational formulation of nonequilibrium thermodynamics…
Many physical systems characterized by nonlinear multiscale interactions can be effectively modeled by treating unresolved degrees of freedom as random fluctuations. However, even when the microscopic governing equations and qualitative…
Complex Langevin dynamics can be used to perform numerical simulations of theories with a complex action. In order to justify the procedure, it is important to understand the properties of the real and positive distribution, which is…
Learning in deep models using Bayesian methods has generated significant attention recently. This is largely because of the feasibility of modern Bayesian methods to yield scalable learning and inference, while maintaining a measure of…
Path-wise observables--functionals of stochastic trajectories--are at the heart of time-average statistical mechanics and are central to thermodynamic inequalities such as uncertainty relations, speed limits, and correlation-bounds. They…
We conduct a thorough study of different forms of horizontally explicit and vertically implicit (HEVI) time-integration strategies for the compressible Euler equations on spherical domains typical of nonhydrostatic global atmospheric…
In this paper, a novel channel modeling approach, named light detection and ranging (LiDAR)-aided geometry-based stochastic modeling (LA-GBSM), is developed. Based on the developed LA-GBSM approach, a new millimeter wave (mmWave) channel…
Overdamped Langevin dynamics are reversible stochastic differential equations which are commonly used to sample probability measures in high-dimensional spaces, such as the ones appearing in computational statistical physics and Bayesian…
For continuous-time linear stochastic dynamical systems driven by Wiener processes, we consider the problem of designing ensemble filters when the observation process is randomly time-sampled. We propose a continuous-discrete McKean--Vlasov…
We consider the parallel time integration of the linear advection equation with the Parareal and two-level multigrid-reduction-in-time (MGRIT) algorithms. Our aim is to develop a better understanding of the convergence behaviour of these…
Diffusion models are state-of-the-art methods in generative modeling when samples from a target probability distribution are available, and can be efficiently sampled, using score matching to estimate score vectors guiding a Langevin…
The full discretization of the semi-linear stochastic wave equation is considered. The discontinuous Galerkin finite element method is used in space and analyzed in a semigroup framework, and an explicit stochastic position Verlet scheme is…
Diffusion models recently developed for generative AI tasks can produce high-quality samples while still maintaining diversity among samples to promote mode coverage, providing a promising path for learning stochastic closure models.…