Surrogate-Based Bayesian Inverse Modeling of the Hydrological System: An Adaptive Approach Considering Surrogate Approximation Error

TL;DR

This paper introduces an adaptive surrogate-based Bayesian inverse modeling framework for hydrological systems that explicitly accounts for and reduces surrogate approximation errors, improving inversion accuracy in complex scenarios.

Contribution

It develops two strategies to quantify and reduce surrogate approximation errors, enhancing Bayesian inverse modeling accuracy in hydrology.

Findings

Both strategies effectively reduce surrogate bias.

The combined approach outperforms individual strategies.

Demonstrated success in high-dimensional, multimodal, and real-world cases.

Abstract

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, 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 to quantify the surrogate error. The first strategy works by quantifying the surrogate prediction uncertainty with a Bayesian method, while the second strategy uses another surrogate to simulate and correct the approximation error of the primary surrogate. 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, multimodality, and a real-world application, it is found that both strategies can reduce the bias introduced by surrogate approximation error, while the second strategy that integrates two methods (i.e., polynomial chaos expansion and Gaussian process in this work) that complement each other shows the best performance.