Related papers: Non-stationary Spatio-Temporal Modeling Using the …
We develop numerical methods for reaction-diffusion systems based on the equations of fluctuating hydrodynamics (FHD). While the FHD formulation is formally described by stochastic partial differential equations (SPDEs), it becomes similar…
Stochastic differential equations (SDEs) provide a natural framework for modelling intrinsic stochasticity inherent in many continuous-time physical processes. When such processes are observed in multiple individuals or experimental units,…
Stochastic and conditional simulation methods have been effective towards producing realistic realizations and simulations of spatial numerical models that share equal probability of occurrence. Application of these methods are valuable…
In employing spatial regression models for counts, we usually meet two issues. First, ignoring the inherent collinearity between covariates and the spatial effect would lead to causal inferences. Second, real count data usually reveal over…
We investigate a spatially discrete surrogate model for the dynamics of a slender, elastic, inextensible fiber in turbulent flows. Deduced from a continuous space-time beam model for which no solution theory is available, it consists of a…
Spatial reaction-diffusion models have been employed to describe many emergent phenomena in biological systems. The modelling technique most commonly adopted in the literature implements systems of partial differential equations (PDEs),…
This article investigates the non-stationary reaction-diffusion-advection equation, emphasizing solutions with internal layers and the associated inverse problems. We examine a nonlinear singularly perturbed partial differential equation…
Explicit numerical finite difference schemes for partial differential equations are well known to be easy to implement but they are particularly problematic for solving equations whose solutions admit shocks, blowups and discontinuities.…
We propose a novel numerical approach for nonlocal diffusion equations [8] with integrable kernels, based on the relationship between the backward Kolmogorov equation and backward stochastic differential equations (BSDEs) driven by L\`{e}vy…
Bayesian models based on Gaussian processes (GPs) offer a flexible framework to predict spatially distributed variables with uncertainty. But the use of nonstationary priors, often necessary for capturing complex spatial patterns, makes…
This is an expository article on the score-based diffusion models, with a particular focus on the formulation via stochastic differential equations (SDE). After a gentle introduction, we discuss the two pillars in the diffusion modeling --…
We develop a novel approach towards causal inference. Rather than structural equations over a causal graph, we learn stochastic differential equations (SDEs) whose stationary densities model a system's behavior under interventions. These…
We consider reaction-diffusion equations that are stochastically forced by a small multiplicative noise term. We show that spectrally stable traveling wave solutions to the deterministic system retain their orbital stability if the…
This paper deals with the problem of efficient sampling from a stochastic differential equation, given the drift function and the diffusion matrix. The proposed approach leverages a recent model for probabilities \cite{rudi2021psd} (the…
Spatio-temporal problems exist in many areas of knowledge and disciplines ranging from biology to engineering and physics. However, solution strategies based on classical statistical techniques often fall short due to the large number of…
In Rajeev (2013), 'Translation invariant diffusion in the space of tempered distributions', it was shown that there is an one to one correspondence between solutions of a class of finite dimensional SDEs and solutions of a class of SPDEs in…
Modelling partial differential equations (PDEs) is of crucial importance in science and engineering, and it includes tasks ranging from forecasting to inverse problems, such as data assimilation. However, most previous numerical and machine…
In this study, a novel semi-implicit second-order temporal scheme combined with the finite element method for space discretization is proposed to solve the coupled system of infiltration and solute transport in unsaturated porous media. The…
In this paper, we develop a second-order accurate time-stepping scheme for the tempered time-fractional advection-dispersion equation based on a sum-of-exponentials (SOE) approximation to the convolution kernel involved in the fractional…
A generator of spatio-temporal pseudo-random Gaussian fields that satisfy the "proportionality of scales" property (Tsyroulnikov, 2001) is presented. The generator is based on a third-order in time stochastic differential equation with a…