Model Reduction in Groundwater Modeling

这是一份提交给NSF和ARO的联合支持的提案，每个机构都被要求为该提案的单独但相关的方面提供资金。我们建议开发可用于模型降阶的技术，从而将复杂的完整模型替换为更小、更简单的近似，从而在期望的精度范围内产生输出。我们提出的方法结合了数据驱动和模型驱动的方法，因为它利用了输入/输出数据关系，并结合了模型的物理特性。这一建议的首要目标是在一维、二维和三维地下水建模中通过适当的正交分解来表述和推广模型简化，并开发基于控制方程结构和模型参数的快照选择协议。我们还将提出将简化模型用于地下水管理以及解决参数估计的逆问题的程序。我们将使用数值实验和真实的案例研究来展示如何使用这种新的、健壮的方法来大幅减少计算需求，同时保持显著的精度。国家科学基金会的工作重点是简化模型的误差分析，这是拟议研究的一个关键组成部分。此外，我们将重点验证拟议的方法，使用现场数据进行参数估计和联合使用地表水和地下水。我们已经与南加州的卡列瓜斯市水区(CMWD)达成了合作安排。

This is a proposal submitted to both NSF and ARO for joint support, with each agency being asked to fund separate but related facets of the proposal. We propose to develop techniques which can be used for model reduction, whereby a complex full-model is replaced with a smaller simpler approximation that produces outputs within a desired degree of accuracy. Our proposed method combines the data driven and model driven methods in that it makes use of input/output data relationships as well as incorporates the physics of the model. The overriding objective of this proposal is to formulate and generalize model reduction via proper orthogonal decomposition in groundwater modeling in one, two, and three dimensions and to develop a protocol for snapshot selection based on the structure of both the governing equation and the parameters of the model. We will also propose procedures whereby the reduced-model is utilized for groundwater management as well as for solving the inverse problem of parameter estimation. We will use numerical experiments and real case studies to show how this new, robust methodology can be used to drastically reduce the computational demand, while maintaining a significant degree of accuracy. The NSF portion of the work focuses on error analysis of the reduced model, which is a key component of the proposed research. Additionally, we will focus on verification of the proposed methodology using field data for parameter estimation and conjunctive use of surface water and groundwater. We have made arrangements with the Calleguas Municipal Water District (CMWD) in southern California for collaboration.