Related papers: Convergence of stochastic structure-preserving sch…
We study the large deviations principle for locally periodic stochastic differential equations with small noise and fast oscillating coefficients. There are three possible regimes depending on how fast the intensity of the noise goes to…
Lagrangian averaging plays an important role in the analysis of wave--mean-flow interactions and other multiscale fluid phenomena. The numerical computation of Lagrangian means, e.g. from simulation data, is however challenging. Typical…
This paper is concerned with a rigorous convergence analysis of a fully discrete Lagrangian scheme for the Hele-Shaw flow, which is the fourth order thin-film equation with linear mobility in one space dimension. The discretization is based…
Stochastic differential equations are an important modeling class in many disciplines. Consequently, there exist many methods relying on various discretization and numerical integration schemes. In this paper, we propose a novel,…
In this paper, we present a new self-supervised scene flow estimation approach for a pair of consecutive point clouds. The key idea of our approach is to represent discrete point clouds as continuous probability density functions using…
This study proposes an algorithm for modeling compressible flows in spherical shells in nearly incompressible and weakly compressible regimes based on an implicit direction splitting approach. The method retains theoretically expected…
In probability density function (PDF) methods of turbulent flows, the joint PDF of several flow variables is computed by numerically integrating a system of stochastic differential equations for Lagrangian particles. A mathematically exact…
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…
Diffusion models have emerged as powerful generative tools with applications in computer vision and scientific machine learning (SciML), where they have been used to solve large-scale probabilistic inverse problems. Traditionally, these…
Propagation characteristics of a wave are defined by the dispersion relationship, from which the governing partial differential equation (PDE) can be recovered. PDEs are commonly solved numerically using the finite-difference (FD) method,…
Stochastic mathematical models are essential tools for understanding and predicting complex phenomena. The purpose of this work is to study the exit times of a stochastic dynamical system-specifically, the mean exit time and the…
We address the problem of simulation and parameter inference for chemical reaction networks described by the chemical Langevin equation, a stochastic differential equation (SDE) representation of the dynamics of the chemical species. This…
The diffusion approximation of stochastic gradient descent (SGD) in current literature is only valid on a finite time interval. In this paper, we establish the uniform-in-time diffusion approximation of SGD, by only assuming that the…
We propose an accurate numerical scheme for approximating the solution of the two dimensional acoustic wave problem. We use machine learning to find a stencil suitable even in the presence of high wavenumbers. The proposed scheme…
In this article we propose two finite element schemes for the Navier-Stokes equations, based on a reformulation that involves differential operators from the de Rham sequence and an advection operator with explicit skew-symmetry in weak…
We use a method based on the lubrication approximation in conjunction with a residual-based mass-continuity iterative solution scheme to compute the flow rate and pressure field in distensible converging-diverging tubes for Navier-Stokes…
We introduce a predictor-corrector discretisation scheme for the numerical integration of a class of stochastic differential equations and prove that it converges with weak order 1.0. The key feature of the new scheme is that it builds up…
A stable numerical solution of the steady Stokes problem requires compatibility between the choice of velocity and pressure approximation that has traditionally proven problematic for meshless methods. In this work, we present a…
This paper concerns the construction and analysis of a numerical scheme for a mixed discrete-continuous fragmentation equation. A finite volume scheme is developed, based on a conservative formulation of a truncated version of the…
Accurate forecasting of spatiotemporal data remains challenging due to complex spatial dependencies and temporal dynamics. The inherent uncertainty and variability in such data often render deterministic models insufficient, prompting a…