Reduced‐Dimensional Gaussian Process Machine Learning for Groundwater Allocation Planning Using Swarm Theory

Abstract

Groundwater management and allocation planning involves a rigorous assessment of the performance of operational decisions such as extraction/injection rates on community and environmental objectives. Maximizing performance through numerical optimization can be essential for high‐value resources and is often computationally infeasible due to long simulation model run times combined with nonconvex objectives and constraints. In order to mitigate these drawbacks, surrogate models can be used in place of complex models during the optimization process. There exist a number of machine learning techniques that can be used to develop a data‐driven surrogate model. However, the curse of dimensionality, common to groundwater management, limits the use of these techniques due to the necessity for large training data sets. Even though it is now possible to handle large data sets, the generation of these data sets themselves remains computationally prohibitive as they require numerous simulations to produce accurate surrogates. In this study, we integrate a dimensionality reduction method using truncated singular value decomposition to reduce the number of decision variables, thereby reducing the size of the training data set needed. Correspondingly, we demonstrate a simple technique for acquiring an approximate minimax Latin Hypercube design from within the subspace. We also implement a novel technique for adaptive resampling through particle swarm optimization in order to maintain accuracy of the surrogate model throughout the optimization process. The resulting accurate surrogate model for the Perth regional aquifer system of Western Australia runs in a matter of seconds. Adopting this approach can produce timely solutions, making formal optimization tractable for practitioners.

Assessing and Managing Large‐Scale Geochemical Impacts From Groundwater Replenishment With Highly Treated Reclaimed Wastewater

“…The understanding of regional-scale flow processes in the Perth Basin is manifested in the Perth Regional Aquifer Model (PRAMS) (CyMod Systems Pty Ltd, 2014;de Silva et al, 2013), which has been jointly developed by the key stakeholders of the groundwater system and is used to underpin a wide range of water management decisions such as groundwater allocations (Siade et al, 2020). The latest calibrated version, PRAMS v3.5.2, uses MODFLOW-2000 (Harbaugh et al, 2000) to simulate groundwater flow, and a groundwater recharge simulator for the vadose zone, the Vertical Flux Model (Dawes et al, 2012), is used to simulate the spatiotemporally varying groundwater recharge to the superficial aquifer.…”

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. In order to maintain accuracy of the surrogate model, a novel adaptive resampling through particle swarm optimization is designed throughout the optimization process.…”

Unraveling biogeochemical complexity through better integration of experiments and modeling

“…49 Machine learning algorithms may also hold the promise of reducing computational costs. 45,63 As the eld of Bayesian inference is rapidly evolving, more efficient techniques can be expected to become available in the future.…”