Stochastic Model-Based Source Identification

In this paper we investigate the use of Stochastic Reduced Order Models (SROMs) for solving Stochastic Source Identification (SSI) problems in steady-state transport phenomena given statistics of the system state at a small number of locations. We capture the physics of the transport phenomenon by a Partial Differential Equation (PDE) which we discretize using the finite element method. The SSI problem is then formulated as a stochastic optimization problem constrained by the PDE, and then transformed into a deterministic one after representing the random quantities with a low-dimensional discrete SROM. The small number of samples given by SROMs requires only a small number of PDE solves at each optimization iteration in order to obtain a solution to the SSI problem, defined as a distribution of possible source locations and intensities. We provide simulations to demonstrate the effectiveness of SROMs in capturing uncertainty. We also demonstrate the ability of SROMs to capture multiple independent sources of uncertainty, in particular, we consider uncertainty in the location of the measurements which has practical implications in robotics applications.