Inverse modeling of hydrologic systems with adaptive multi-fidelity simulations
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Markov chain Monte Carlo (MCMC) simulation methods are widely used to assess parameter uncertainties of hydrologic models conditioned on measurements of observable state variables. However, when the model is CPU-intensive, 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. When integrating the high and low-fidelity models in a proper manner, we can balance both efficiency and accuracy in the MCMC simulation. As the posterior distribution of the unknown model parameters is the region of our interest, it is wise to distribute most of the computational budget therein. Based on this idea, we propose an adaptive multi-fidelity simulation-based MCMC algorithm for efficient inverse modeling of hydrologic systems in this paper. Here, we evaluate the high-fidelity model mainly in the posterior region through iteratively running MCMC based on a Gaussian process (GP) system adaptively constructed with multi-fidelity simulations. The error of the GP system is rigorously considered in the MCMC simulations and gradually reduced to a negligible level. Thus, the proposed method can obtain an accurate estimate of the posterior distribution with a very low computational cost, whose performance is demonstrated by two numerical case studies in inverse modeling of hydrologic systems.
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