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- Title
Reduced Geostatistical Approach With a Fourier Neural Operator Surrogate Model for Inverse Modeling of Hydraulic Tomography.
- Authors
Guo, Quan; He, Yu; Liu, Ming; Zhao, Yue; Liu, Yuzheng; Luo, Jian
- Abstract
In this study, we propose a new approach for inverse modeling of hydraulic tomography (HT) using the Fourier neural operator (FNO) as a surrogate forward model. FNO is a deep learning model that directly parameterizes the integral kernel in Fourier space to learn solution operators for parametric partial differential equations (PDEs). We trained a highly accurate FNO to learn the solution operators of PDEs in HT, which can efficiently generate multiple channels of hydraulic head fields corresponding to specific pumping tests in new parameter fields through a single forward pass. The trained FNO surrogate model is integrated with the reduced geostatistical approach (RGA) to provide a powerful tool, named RGA‐FNO, for inverse modeling of Gaussian random fields. RGA utilizes principal components to effectively reduce problem dimensions and encode geostatistical information. FNO benefits from deep learning automatic differentiation, enabling efficient backpropagation of gradients during inverse modeling. Our results show that RGA‐FNO can efficiently produce satisfactory estimations for random transmissivity fields with an exponential covariance function, which is non‐differentiable and visually non‐smooth. The RGA‐FNO application on steady‐state multi‐well HT is better than the single‐well transient pumping test for inverse modeling. The data required for inverse modeling applications of RGA‐FNO increases with the variance of the random transmissivity fields. FNO and other neural operator models have the potential to play an important role in groundwater modeling, especially in inverse modeling and experimental design, which often requires a large number of forward simulations. Key Points: RGA‐FNO integrates the reduced geostatistical approach (RGA) with a Fourier neural operator (FNO) surrogate modelA highly accurate FNO was trained to learn the solution operators of PDEs in hydraulic tomography, generating multiple hydraulic head dataRGA‐FNO can efficiently produce satisfactory estimations for random transmissivity fields with high‐rank, small‐scale heterogeneities
- Subjects
HYDRAULIC models; PARTIAL differential operators; DEEP learning; RANDOM fields; TOMOGRAPHY; PARTIAL differential equations; GEOLOGICAL statistics
- Publication
Water Resources Research, 2024, Vol 60, Issue 6, p1
- ISSN
0043-1397
- Publication type
Article
- DOI
10.1029/2023WR034939