Related papers: Nonlinear Filtering and Spatial Asymptotic Consist…

The filtering distribution is a time-evolving probability distribution on the state of a dynamical system, given noisy observations. We study the large-time asymptotics of this probability distribution for discrete-time, randomly…

Spatially distributed problems are often approximately modelled in terms of partial differential equations (PDEs) for appropriate coarse-grained quantities (e.g. concentrations). The derivation of accurate such PDEs starting from finer…

Discrete time control systems whose dynamics and observations are described by stochastic equations are common in engineering, operations research, health care, and economics. For example, stochastic filtering problems are usually defined…

We study inverse boundary problems for evolutionary PDEs using only a single passive boundary observation, where data from an unknown internal source propagate through an unknown medium without active inputs. The goal is the simultaneous…

This paper considers the filtering problem which consists in reconstructing the state of a dynamical system with partial observations coming from sensor measurements, and the knowledge that the dynamics are governed by a physical PDE model…

Spatiotemporal dynamics models are fundamental for various domains, from heat propagation in materials to oceanic and atmospheric flows. However, currently available neural network-based spatiotemporal modeling approaches fall short when…

Advances in cellular imaging technologies, especially those based on fluorescence in situ hybridization (FISH) now allow detailed visualization of the spatial organization of human or bacterial cells. Quantifying this spatial organization…

Structural monitoring for complex built environments often suffers from mismatch between design, laboratory testing, and actual built parameters. Additionally, real-world structural identification problems encounter many challenges. For…

Many physical processes can be expressed through partial differential equations (PDEs). Real-world measurements of such processes are often collected at irregularly distributed points in space, which can be effectively represented as…

This review maps developments in stochastic modeling, highlighting non-standard approaches and their applications to biology and epidemiology. It brings together four strands: (1) core models for systems that evolve with randomness; (2)…

The measured spatiotemporal response of various physical processes is utilized to infer the governing partial differential equations (PDEs). We propose SimultaNeous Basis Function Approximation and Parameter Estimation (SNAPE), a technique…

The filtering distribution captures the statistics of the state of a dynamical system from partial and noisy observations. Classical particle filters provably approximate this distribution in quite general settings; however they behave…

We study a linear filtering problem where the signal and observation processes are described as solutions of linear stochastic differential equations driven by time-space Brownian sheets. We derive a stochastic integral equation for the…

This survey paper is written with the intention of giving a mathematical introduction to filtering techniques for intermittent data assimilation, and to survey some recent advances in the field. The paper is divided into three parts. The…

This paper discusses infill asymptotics for logistic regression estimators for spatio-temporal point processes whose intensity functions are of log-linear form. We establish strong consistency and asymptotic normality for the parameters of…

Estimation of the covariance structure of spatial processes is of fundamental importance in spatial statistics. In the literature, several non-parametric and semi-parametric methods have been developed to estimate the covariance structure…

Reconstructing PDE solutions from sparse observations is a core challenge in scientific computing. We present FM4PDE, a flow-matching generative framework that learns the joint distribution of PDE coefficients (or initial states) and…

This paper is concerned with the mathematical analysis of continuous time Ensemble Kalman Filters (EnKBFs) and their mean field limit in an infinite dimensional setting. The signal is determined by a nonlinear Stochastic Partial…

In this paper we present a mathematical study of particle diffusion inside and outside a spherical biological cell that has been exposed on one side to a propagating planar diffusive front. The media inside and outside the spherical cell…

In the past, we have presented a systematic computational framework for analyzing self-similar and traveling wave dynamics in nonlinear partial differential equations (PDEs) by dynamically factoring out continuous symmetries such as…