Nonlinear Reduced Order Source Identification under Uncertainty

We propose a tractable stochastic model-based approach for identification of chemical sources that relies on the Advection-Diffusion (AD) PDE to model the transport phenomenon and utilizes Markov Chain Monte Carlo sampling to obtain the posterior distribution of the source parameters considering uncertainty in the parameters of the PDE and the sensor data. To make the algorithm tractable, we model the sources using nonlinear basis functions and utilize a model reduction method to obtain closed-form approximate solutions for the AD-PDE. The former idea drastically reduces the dimension of the sampling space while the latter facilitates the evaluation of the likelihood function. We present extensive numerical experiments that demonstrate that our algorithm can estimate the desired source parameters and provide uncertainty bounds for them.