Physics-Guided Neural Networks for Distributed Sparse Gas Source Localization Using Poisson's Equation and Green's Function Method

Finding sources or leaks of airborne material in Chemical, Biological, Radiological, or Nuclear (CBRN) accidents is crucial for effective disaster response. This paper makes use of sparse Bayesian learning (SBL) to cooperatively estimate source locations based on measurements by multiple robots or a sensor network. The SBL approach facilitates the identification of sparse source support, indirectly providing information about the number of sources and their locations. To achieve this, we introduce a novel method that includes a trained surrogated model for the gas dispersion process described by a Partial Differential Equation (PDE). Namely, a Physics-Guided Neural Network (PGNN) is employed to approximate a parameterized Green's function of the PDE. The obtained approximation is integrated into a gradient-based optimization process. The proposed method allows estimating super-resolution arbitrary source locations, eliminating constraints to a specific grid. Further, the newly proposed PGNN surrogate model comes with the advantage that the approach can be extended to cases where no analytic Green's function is available. Simulation results demonstrate the effectiveness of the proposed approach, showcasing its potential for enhanced airborne material detection in CBRN scenarios.