Inverse source problem in a forced network

TL;DR

This paper presents a method to uniquely identify a time-dependent source in a network governed by a wave equation using minimal measurements, and develops a non-iterative approach for localization and signal identification.

Contribution

It introduces a novel non-iterative method for localizing the source node and identifying the emitted signal in a network governed by a wave equation.

Findings

The method guarantees uniqueness of source localization with measurements at two nodes.

Numerical experiments confirm the effectiveness of the proposed approach on a 5-node graph.

The approach successfully identifies both source position and emitted signal.

Abstract

We address the nonlinear inverse source problem of identifying a time-dependent source occurring in one node of a network governed by a wave equation. We prove that time records of the associated state taken at a strategic set of two nodes yield uniqueness of the two unknown elements: the source position and the emitted signal. We develop a non-iterative identification method that localizes the source node by solving a set of well posed linear systems. Once the source node is localized, we identify the emitted signal using a deconvolution problem or a Fourier expansion. Numerical experiments on a $5$ node graph confirm the effectiveness of the approach.