相关论文: Deformed SPDE models with an application to spatia…

Travelling and rotating waves are ubiquitous phenomena observed in time dependent PDEs modelling the combined effect of dissipation and non-linear interaction. From an abstract viewpoint they appear as relative equilibria of an equivariant…

This paper deals with the numerical approximation of semilinear parabolic stochastic partial differential equation (SPDE) driven simultaneously by Gaussian noise and Poisson random measure, more realistic in modeling real world phenomena.…

Optimizing over the stationary distribution of stochastic differential equations (SDEs) is computationally challenging. A new forward propagation algorithm has been recently proposed for the online optimization of SDEs. The algorithm solves…

We investigate the stationary state of a model system evolving according to a modified focusing truncated nonlinear Schr\"odinger equation (NLSE) used to describe the envelope of Langmuir waves in a plasma. We restrict the system to have a…

Precipitation exceedance probabilities are widely used in engineering design, risk assessment, and floodplain management. While common approaches like NOAA Atlas 14 assume that extreme precipitation characteristics are stationary over time,…

We develop a new continuous-time stochastic gradient descent method for optimizing over the stationary distribution of stochastic differential equation (SDE) models. The algorithm continuously updates the SDE model's parameters using an…

We introduce a novel paradigm for learning non-parametric drift and diffusion functions for stochastic differential equation (SDE). The proposed model learns to simulate path distributions that match observations with non-uniform time…

Traditional partial differential equations with constant coefficients often struggle to capture abrupt changes in real-world phenomena, leading to the development of variable coefficient PDEs and Markovian switching models. Recently,…

We consider a nonlinear stochastic partial differential equation (SPDE) in divergence form where the forcing term is a Gaussian noise, that is white in time and colored in space such that the gradient of the solution is H\"older-continuous,…

The coefficients in a second order parabolic linear stochastic partial differential equation (SPDE) are estimated from multiple spatially localised measurements. Assuming that the spatial resolution tends to zero and the number of…

In this paper, we develop the mathematical framework for filtering problems arising from biophysical applications where data is collected from confocal laser scanning microscopy recordings of the space-time evolution of intracellular wave…

Nonstationarity is a major challenge in analyzing spatial data. For example, daily precipitation measurements may have increased variability and decreased spatial smoothness in areas with high mean rainfall. Common nonstationary covariance…

Spatial Gaussian fields (SGFs) are widely employed in modeling the distributions of marine megafauna, yet they traditionally rely on assumptions of isotropy and stationarity, conditions that often prove unrealistic in complex ecological…

In this paper, we study large and moderate deviation principles for stochastic partial differential equations (SPDEs) on metric graphs and their associated multiscale models via the weak convergence approach, providing a refined…

We develop an unsupervised machine learning algorithm for the automated discovery and identification of traveling waves in spatio-temporal systems governed by partial differential equations (PDEs). Our method uses sparse regression and…

This paper aims to extend the Besag model, a widely used Bayesian spatial model in disease mapping, to a non-stationary spatial model for irregular lattice-type data. The goal is to improve the model's ability to capture complex spatial…

We study the dynamics of a continuous-time model of the Stochastic Gradient Descent (SGD) for the least-square problem. Indeed, pursuing the work of Li et al. (2019), we analyze Stochastic Differential Equations (SDEs) that model SGD either…

In this paper, the stability of fractional differential equations (FDEs) with unknown parameters is studied. FDEs bring many advantages to model the physical systems in the nature or man-made systems in the industry. Because this…

It is increasingly understood that the assumption of stationarity is unrealistic for many spatial processes. In this article, we combine dimension expansion with a spectral method to model big non-stationary spatial fields in a…

In this study, a Fourier-based, split-step Pad\'e (SSP) method for solving the parabolic wave equation with applications in guided wave propagation in ocean acoustics is presented. Traditional SSP implementations rely in finite-difference…