Inverse modeling of hydrologic systems with adaptive multi-fidelity Markov chain Monte Carlo simulations

Markov chain Monte Carlo (MCMC) simulation methods are widely used to assess parametric uncertainties of hydrologic models conditioned on measurements of observable state variables. However, when the model is CPU-intensive and high-dimensional, the computational cost of MCMC simulation will be prohibitive. In this situation, a CPU-efficient while less accurate low-fidelity model (e.g., a numerical model with a coarser discretization, or a data-driven surrogate) is usually adopted. Nowadays, multi-fidelity simulation methods that can take advantage of both the efficiency of the low-fidelity model and the accuracy of the high-fidelity model are gaining popularity. In the MCMC simulation, as the posterior distribution of the unknown model parameters is the region of interest, it is wise to distribute most of the computational budget (i.e., the high-fidelity model evaluations) therein. Based on this idea, in this paper we propose an adaptive multi-fidelity MCMC algorithm for efficient inverse modeling of hydrologic systems. In this method, we evaluate the high-fidelity model mainly in the posterior region through iteratively running MCMC based on a Gaussian process (GP) system that is adaptively constructed with multi-fidelity simulation. The error of the GP system is rigorously considered in the MCMC simulation and gradually reduced to a negligible level in the posterior region. Thus, the proposed method can obtain an accurate estimate of the posterior distribution with a small number of the high-fidelity model evaluations. The performance of the proposed method is demonstrated by three numerical case studies in inverse modeling of hydrologic systems.