# Modeling and Computation Seminar

### Inverse source problem in a forced network

### 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. This is an important problem for applications like monitoring the electrical grid or testing a network of acoustic pipes. 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. Using graph theory, we discuss the number and location of the observation nodes. A non-iterative identification method that localizes the source node by solving a set of well posed linear systems is developped. Once the source node is localized, the emitted signal is identified using a deconvolution problem or a Fourier expansion. Numerical experiments on a five node graph confirm the feasability of the approach.