Source Reconstruction for Spatio-Temporal Physical Statistical Models

TL;DR

This paper introduces a general statistical method to reconstruct unknown source terms in linear PDEs from measurements affected by complex fluid dynamics, with applications in environmental pollution analysis.

Contribution

The paper presents a novel, general approach for source reconstruction in linear PDE models, applicable to various physical systems affected by fluid dynamics.

Findings

Effective source reconstruction demonstrated on simulated data.

Applicable to any linear PDE with complex boundary conditions.

Potential for real-world environmental pollution monitoring.

Abstract

In many applications, a signal is deformed by well-understood dynamics before it can be measured. For example, when a pollutant enters a river, it immediately begins dispersing, flowing, settling, and reacting. If the pollutant enters at a single point, its concentration can be measured before it enters the complex dynamics of the river system. However, in the case of a non-point source pollutant, it is not clear how to efficiently measure its source. One possibility is to record concentration measurements in the river, but this signal is masked by the fluid dynamics of the river. Specifically, concentration is governed by the advection-diffusion-reaction PDE, with an unknown source term. We propose a method to statistically reconstruct a source term from these PDE-deformed measurements. Our method is general and applies to any linear PDE. This method has important applications in the study of environmental DNA and non-point source pollution.