Surrogate-Based Bayesian Inverse Modeling of the Hydrological System: An Adaptive Approach Considering Surrogate Structural Error
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Inverse modeling is vital for an improved hydrological prediction. However, this process can be computationally demanding as it usually requires a large number of model evaluations. To address this issue, one can take advantage of surrogate modeling techniques, e.g., the one based on sparse polynomial chaos expansion (PCE). Nevertheless, when structural error of the surrogate model is neglected in inverse modeling, the inversion results will be biased. In this paper, we develop a surrogate-based Bayesian inversion framework that rigorously quantifies and gradually eliminates the structural error of the surrogate. Specifically, two strategies are proposed and compared. The first strategy works by obtaining an ensemble of sparse PCE surrogates with Markov chain Monte Carlo sampling, while the second one uses Gaussian process (GP) to simulate the structural error of a single sparse PCE surrogate. With an active learning process, the surrogate structural error can be gradually reduced to a negligible level in the posterior region, where the original input-output relationship can be much more easily captured by PCE than in the prior. Demonstrated by one numerical case of groundwater contaminant source identification with 28 unknown input variables, it is found that both strategies can efficiently reduce the bias introduced by surrogate modeling, while the second strategy has a better performance as it integrates two methods (i.e., PCE and GP) that complement each other.
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