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  1. Free, publicly-accessible full text available October 2, 2024
  2. Coupled partial differential equations (PDEs) are key tasks in modeling the complex dynamics of many physical processes. Recently, neural operators have shown the ability to solve PDEs by learning the integral kernel directly in Fourier/Wavelet space, so the difficulty for solving the coupled PDEs depends on dealing with the coupled mappings between the functions. Towards this end, we propose a coupled multiwavelets neural operator (CMWNO) learning scheme by decoupling the coupled integral kernels during the multiwavelet decomposition and reconstruction procedures in the Wavelet space. The proposed model achieves significantly higher accuracy compared to previous learning-based solvers in solving the coupled PDEs including Gray-Scott (GS) equations and the non-local mean field game (MFG) problem. According to our experimental results, the proposed model exhibits a 2ˆ „ 4ˆ improvement relative L2 error compared to the best results from the state-of-the-art models. 
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    Free, publicly-accessible full text available April 1, 2024
  3. Abstract

    Aquifers supporting irrigated agriculture are a resource of global importance. Many of these systems, however, are experiencing significant pumping‐induced stress that threatens their continued viability as a water source for irrigation. Reductions in pumping are often the only option to extend the lifespans of these aquifers and the agricultural production they support. The impact of reductions depends on a quantity known as “net inflow” or “capture.” We use data from a network of wells in the western Kansas portions of the High Plains aquifer in the central United States to demonstrate the importance of net inflow, how it can be estimated in the field, how it might vary in response to pumping reductions, and why use of “net inflow” may be preferred over “capture” in certain contexts. Net inflow has remained approximately constant over much of western Kansas for at least the last 15 to 25 years, thereby allowing it to serve as a target for sustainability efforts. The percent pumping reduction required to reach net inflow (i.e., stabilize water levels for the near term [years to a few decades]) can vary greatly over this region, which has important implications for groundwater management. However, the reduction does appear practically achievable (less than 30%) in many areas. The field‐determined net inflow can play an important role in calibration of regional groundwater models; failure to reproduce its magnitude and temporal variations should prompt further calibration. Although net inflow is a universally applicable concept, the reliability of field estimates is greatest in seasonally pumped aquifers.

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