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Stochastic simulation algorithms such as likelihood weighting often give fast, accurate approximations to posterior probabilities in probabilistic networks, and are the methods of choice for very large networks. Unfortunately, the special…
We study the stochastic Leray-{\alpha} model of Euler equations with transport noise. We first use weak convergence approach to show the large deviations of the stochastic Leray-{\alpha} model of Euler equations in a suitable scaling limit.…
We present strongly convergent explicit and semi-implicit adaptive numerical schemes for systems of stiff stochastic differential equations (SDEs) where both the drift and diffusion are non-globally Lipschitz continuous. This stiffness may…
In this paper, we investigate the problem of strong approximation of the solutions of stochastic differential equations (SDEs) when the drift coefficient is given in integral form. We investigate its upper error bounds, in terms of the…
The use of spectral proper orthogonal decomposition (SPOD) to construct low-order models for broadband turbulent flows is explored. The choice of SPOD modes as basis vectors is motivated by their optimality and space-time coherence…
Two dimensional stochastic time model of scrape-off layer (SOL) turbulent transport is studied. Instability arisen in the system with respect to the stochastic perturbations of both either density or vorticity reveals itself in the strong…
Many stochastic differential equations (SDEs) in the literature have a superlinearly growing nonlinearity in their drift or diffusion coefficient. Unfortunately, moments of the computationally efficient Euler-Maruyama approximation method…
We present a framework and algorithms to learn controlled dynamics models using neural stochastic differential equations (SDEs) -- SDEs whose drift and diffusion terms are both parametrized by neural networks. We construct the drift term to…
We obtain new transport-entropy inequalities and, as a by-product, new deviation estimates for the laws of two kinds of discrete stochastic approximation schemes. The first one refers to the law of an Euler like discretization scheme of a…
We establish a general theory of optimal strong error estimation for numerical approximations of a second-order parabolic stochastic partial differential equation with monotone drift driven by a multiplicative infinite-dimensional Wiener…
There is an emerging need for efficient solutions to stochastic AC Optimal Power Flow ({AC-}OPF) to ensure optimal and reliable grid operations in the presence of increasing demand and generation uncertainty. This paper presents a highly…
We describe an Euler scheme to approximate solutions of L\'evy driven Stochastic Differential Equations (SDE) where the grid points are random and given by the arrival times of a Poisson process. This result extends a previous work of the…
In this work we consider solutions to stochastic partial differential equations with transport noise, which are known to converge, in a suitable scaling limit, to solution of the corresponding deterministic PDE with an additional viscosity…
The Schr\"odinger bridge problem is concerned with finding a stochastic dynamical system bridging two marginal distributions that minimises a certain transportation cost. This problem, which represents a generalisation of optimal transport…
Statistical solutions of incompressible Euler describe turbulent dynamics as time-parameterized laws on $L^2$ whose multi-point correlations satisfy an infinite hierarchy of weak identities. Modern generative samplers for PDE forecasting…
We consider the long-time behavior of an explicit tamed Euler scheme applied to a class of stochastic differential equations driven by additive noise, under a one-sided Lipschitz continuity condition. The setting encompasses drift…
I propose a novel framework that integrates stochastic differential equations (SDEs) with deep generative models to improve uncertainty quantification in machine learning applications involving structured and temporal data. This approach,…
We propose a new framework for generative modeling based on a discrete-time stochastic control formulation of measure transport. Adapting classic results from control theory, we formulate our problem as a linear program whose dual variables…
Small-scale features of shallow water flow obtained from direct numerical simulation (DNS) with two different computational codes for the shallow water equations are gathered offline and subsequently employed with the aim of constructing a…
This work investigates variational frameworks for modeling stochastic dynamics in incompressible fluids, focusing on large-scale fluid behavior alongside small-scale stochastic processes. The authors aim to develop a coupled system of…