Nonlinear reduced order source identification
In this paper we propose a novel approach to the problem of model-based source identification in steady-state transport phenomena given a set of noisy measurements. We formulate the problem as an optimization problem in function space and utilize the adjoint method to calculate the gradient. To obtain a finite dimensional representation of this problem we employ proper orthogonal decomposition, which provides a small number of basis functions that best approximate the function space in which the concentration function lives. Similarly, we parametrize the source function by nonlinear tower functions, which allow us to reduce the size of the problem from thousands of unknowns to a handful of variables. The above approximations give rise to a low dimensional nonlinear optimization problem, for which we provide explicit expressions for the gradient and Hessian that can be used with available optimization techniques to solve for the desired source function. We provide simulation results that demonstrate a drastic reduction in computation time. At the same time we are able to solve complex advection-diffusion problems in non-convex environments.
