A Probabilistic Approach to Inverse Convection-Diffusion

Initial condition inverse problems are ill-posed and computationally expensive to solve. We present a computational approach for solving inverse problems in the realm of one-dimensional contaminant transport. The approach employs finite differencing as a forward solver and probabilistic methods for inversion. Markov Chain Monte Carlo sampling is used to efficiently recover posterior probabilities. The results show that the Bayesian framework is a robust approach for initial condition inversion. I