Distributed Reduced Order Source Identification

In this paper we propose a distributed approach for model-based Source Identification (SI) that minimizes communication cost and allows for on demand balancing of computational resources, based on the specifications of the sensors. Specifically, we consider the steady-state Advection-Diffusion equation which we discretize using the Finite Element (FE) method, and then apply Proper Orthogonal Decomposition to reduce the order of the model. The concentration measurements that are needed to solve the SI problem are collected by a team of mobile sensors that move in pre-assigned subdomains in the environment. We formulate an $\ell_{2}$-regularized least squares optimization problem that the sensors solve in a distributed way using the Accelerated Distributed Augmented Lagrangian method. Our formulation results in an algorithm whose communication cost is independent of the FE mesh size and its time complexity grows only linearly with it. We present simulation results that show that the proposed method can handle large-scale SI problems and compare our formulation to an alternative derivation using Alternating Direction Method of Multipliers.