Surrogate-Based Bayesian Inverse Modeling of the Hydrological System: An Adaptive Approach Considering Surrogate Approximation Erro
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Bayesian inverse modeling is important for a better understanding of hydrological processes. However, this approach 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. Nevertheless, when approximation error of the surrogate model is neglected in inverse modeling, the inversion result will be biased. In this paper, we develop a surrogate-based Bayesian inversion framework that explicitly quantifies and gradually reduces the approximation error of the surrogate. Specifically, two strategies are proposed and compared. The first strategy works by obtaining an ensemble of sparse polynomial chaos expansion (PCE) surrogates with Markov chain Monte Carlo sampling, while the second one uses Gaussian process (GP) to simulate the approximation error of a single sparse PCE surrogate. The two strategies can also be applied with other surrogates, thus they have general applicability. By adaptively refining the surrogate over the posterior distribution, we can gradually reduce the surrogate approximation error to a small level. Demonstrated with three case studies involving high-dimensionality, multi-modality and a real-world application, respectively, it is found that both strategies can reduce the bias introduced by surrogate modeling, while the second strategy has a better performance as it integrates two methods (i.e., sparse PCE and GP) that complement each other.
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