Related papers: Resonance based schemes for SPDEs
Stochastic differential equations (SDEs) and stochastic partial differential equations (SPDEs) are fundamental for modeling stochastic dynamics across the natural sciences and modern machine learning. Learning their solution operators with…
Stochastic optimisation algorithms are the de facto standard for machine learning with large amounts of data. Handling only a subset of available data in each optimisation step dramatically reduces the per-iteration computational costs,…
In Score based Generative Modeling (SGMs), the state-of-the-art in generative modeling, stochastic reverse processes are known to perform better than their deterministic counterparts. This paper delves into the heart of this phenomenon,…
A system's internal dynamics and its interaction with the environment can be determined by tracking how external perturbations affect its transition rates between states. Quantitative measurements of these rates are crucial for optimizing…
This paper analyzes the convergence for a large class of Riemannian stochastic approximation (SA) schemes, which aim at tackling stochastic optimization problems. In particular, the recursions we study use either the exponential map of the…
Despite their ubiquity throughout science and engineering, only a handful of partial differential equations (PDEs) have analytical, or closed-form solutions. This motivates a vast amount of classical work on numerical simulation of PDEs and…
Parametric model order reduction using reduced basis methods can be an effective tool for obtaining quickly solvable reduced order models of parametrized partial differential equation problems. With speedups that can reach several orders of…
We present the validity of stochastic averaging principle for non-autonomous slow-fast stochastic differential equations (SDEs) whose fast motions admit random periodic solutions. Our investigation is motivated by some problems arising from…
In this study, we introduce a refined method for ascertaining error estimations in numerical simulations of dynamical systems via an innovative application of composition techniques. Our approach involves a dual application of a basic…
We study fully nonlinear second-order (forward) stochastic partial differential equations (SPDEs). They can also be viewed as forward path-dependent PDEs (PPDEs) and will be treated as rough PDEs (RPDEs) under a unified framework. We…
This article proposes and analyzes explicit and easily implementable temporal numerical approximation schemes for additive noise-driven stochastic partial differential equations (SPDEs) with polynomial nonlinearities such as, e.g.,…
The time discretization of stochastic spectral fractional wave equation is studied by using the difference methods. Firstly, we exploit rectangle formula to get a low order time discretization, whose the strong convergence order is smaller…
In this contribution, we introduce numerical continuation methods and bifurcation theory, techniques which find their roots in the study of dynamical systems, to the problem of tracing the parameter dependence of bound and resonant states…
Non-Markovian stochastic Schr\"odinger equations (NMSSE) are important tools in quantum mechanics, from the theory of open systems to foundations. Yet, in general, they are but formal objects: their solution can be computed numerically only…
Partial Differential Equations (PDEs) with high dimensionality are commonly encountered in computational physics and engineering. However, finding solutions for these PDEs can be computationally expensive, making model-order reduction…
Stochastic orders are binary relations defined on probability distributions which capture intuitive notions like being larger or being more variable. This paper introduces stochastic ordering of instantaneous SNRs of fading channels as a…
In this paper, a weak Local Linearization scheme for Stochastic Differential Equations (SDEs) with multiplicative noise is introduced. First, for a time discretization, the solution of the SDE is locally approximated by the solution of the…
Turbulent dynamical systems characterized by both a high-dimensional phase space and a large number of instabilities are ubiquitous among many complex systems in science and engineering. The existence of a strange attractor in the turbulent…
We introduce a novel approach to numerical approximation of nonlinear Schr\"odinger equation with white noise dispersion in the regime of low-regularity solutions. Approximating such solutions in the stochastic setting is particularly…
Projection-based reduced order models are effective at approximating parameter-dependent differential equations that are parametrically separable. When parametric separability is not satisfied, which occurs in both linear and nonlinear…