A Taylor Expansion‐Based Adaptive Design Strategy for Global Surrogate Modeling With Applications in Groundwater Modeling

Abstract

Global sensitivity analysis (GSA) and uncertainty quantification (UQ) for groundwater modeling are challenging because of the model complexity and significant computational requirements. To reduce the massive computational cost, a cheap‐to‐evaluate surrogate model is usually constructed to approximate and replace the expensive groundwater models in the GSA and UQ. Constructing an accurate surrogate requires actual model simulations on a number of parameter samples. Thus, a robust experimental design strategy is desired to locate informative samples so as to reduce the computational cost in surrogate construction and consequently to improve the efficiency in the GSA and UQ. In this study, we develop a Taylor expansion‐based adaptive design (TEAD) that aims to build an accurate global surrogate model with a small training sample size. TEAD defines a novel hybrid score function to search informative samples, and a robust stopping criterion to terminate the sample search that guarantees the resulted approximation errors satisfy the desired accuracy. The good performance of TEAD in building global surrogate models is demonstrated in seven analytical functions with different dimensionality and complexity in comparison to two widely used experimental design methods. The application of the TEAD‐based surrogate method in two groundwater models shows that the TEAD design can effectively improve the computational efficiency of GSA and UQ for groundwater modeling.

Deep Autoregressive Neural Networks for High‐Dimensional Inverse Problems in Groundwater Contaminant Source Identification

“…As a result, in previous studies the surrogate methods were applied either in relatively low‐dimensional (<110) problems or relatively simple flow models (e.g., Ju et al, ; Laloy et al, ; Liao & Zhang, ; Liao et al, ; Lin & Tartakovsky, ; Ma & Zabaras, ; Zeng et al, ; Zhang et al, , ). One approach to alleviate the computational burden is to use adaptivity for selecting informative training samples for surrogate construction (e.g., Mo et al, ; Mo, Shi, et al, ; Zhang et al, ). Such adaptive strategies can somewhat reduce the number of training samples, but the improvement is relatively limited for high‐dimensional problems.…”

Surrogate‐Based Joint Estimation of Subsurface Geological and Relative Permeability Parameters for High‐Dimensional Inverse Problem by Use of Smooth Local Parameterization

“…To further mitigate the computational burden and approximate errors, in the recent years many strategies have been introduced to enable efficient data-driven model reconstruction, for example, compressed sensing, adaptive and/or multilevel, and multifidelity strategies (Gong et al, 2016;Ju et al, 2018;Laloy et al, 2013;Mo et al, 2017;Zhang et al, 2017Zhang et al, , 2018Zhang et al, , 2020Zhou et al, 2018). For example, Adam et al (2020) incorporate a TSVD (truncated singular value decomposition)-based dimensionality reduction method to reduce the number of variables and thereby decrease the HFM runs needed in GPR surrogate.…”

Improved Nested Sampling and Surrogate‐Enabled Comparison With Other Marginal Likelihood Estimators

“…The adaptive construction re‐uses the samples generated during the NSE iterations to re‐estimate the posterior distribution, as the samples are close to the approximate posterior peaks. It would be interesting to compare the adaptive surrogate construction using generalized polynomial chaos with the adaptive surrogate construction using sparse grid stochastic collocation (and other adaptive approaches, e.g., Mo et al, ), although the comparison is beyond the scope of this study.…”