Data-Driven Multiscale Model Identification and Scaling via Random Renormalization Group Operators for Subsurface Transport

水文地质地层中人为污染物弥散（混合）增强的主要原因之一是多尺度非均质性，这在许多情况下导致异常弥散（异常意味着非布朗，即该过程不具备以下至少一种：平稳增量、高斯增量或独立增量）。非均质性可能与水力导电性、孔隙度、吸附性、裂缝和差异膨胀等因素的时空变化有关。自然和人为的非均质性（如压裂过程中发生的非均质性）使得对地下污染物运动的精确建模成为一个极具挑战性的问题。已经提出了许多不同的模型来捕捉与水文运输相关的行为。其中包括布朗运动和列维运动以及这些过程的分数版本。此外，这些模型以其他随机过程（从属）和非线性时钟（时间变换）为条件。当两个或两个以上的模型被合并（求和）时，驱动异常色散的多尺度非均质性可以被解释。拟议的研究将采用统计物理学的工具，确定最佳模型，并开发用户友好的软件，该软件依赖于给定地点的现有数据。如果使用非常丰富的模型，则很容易过度拟合数据。如果使用不那么丰富的模型，它可能无法完全捕获所考虑的行为。所提出的技术通过考虑从非常简单到极其复杂的一系列模型以及介于两者之间的许多模型，规避了这个问题。开发用于识别模型数据的代码将在开源软件许可下发布，教程将编写并提供，以使代码的使用尽可能容易。世界的很大一部分？there’我们的淡水资源位于地球的上部。年代地壳;大约是地球体积的30倍？淡水是地表水。最重要的是，一半的美国人依赖地下水作为家庭用水。因此，为了保护这一宝贵的自然资源，我们必须了解并能够预测人为污染物如何在地下传播。提出的研究通过基于自然地质构造的可用数据创建最佳模型识别方案并随后将结果软件开源来解决这个基本问题。

One of the major contributors to enhanced dispersion (mixing) of anthropogenic contaminants in hydrogeological formations is multiscale heterogeneity, which in many cases leads to anomalous dispersion (anomalous means non-Brownian, i.e., the process does not possess at least one of the following: stationary increments, Gaussian increments or independent increments.) Heterogeneity may be associated with spatial/temporal variations in hydraulic conductivity, porosity, sorbtivity, fractures, and differential swelling to name a few contributors. Natural and man-made (such as occurs during fracking) heterogeneity makes accurate modeling of contaminant movement in the subsurface an extremely challenging problem. A number of disparate models have been proposed to capture behavior associated with hydrologic transport. These include Brownian and Levy motion and fractional versions of these processes. Additionally, these models have been conditioned on other random processes (subordination) and non-linear clocks (time transformations) have been introduced. When two or more of these models are combined (summed), multiscale heterogeneity that drives anomalous dispersion can be accounted for. The proposed research will employ tools from statistical physics, identify optimal models and develop user friendly software which relies on available data for a given site. If a very rich model is used, it can be easy to over fit data. If a less rich model is used, it may not be fully capable of capturing the behavior under consideration. The proposed techniques circumvent this problem by considering a cascade of models that range from the very simple to the extremely complex and many models in between. The codes developed to identify data with models will be released under open source software licenses and tutorials will be written and made available to make the use of the codes as easy as possible.A large portion of the world?s fresh water resources reside in the upper portion of the Earth?s crust; approximately 30 times the volume of the world?s fresh surface water. Most importantly, half of the U.S. population relies on ground water for domestic use. Thus to protect this precious natural resource it is imperative that we understand and can predict how anthropogenic contaminants spread in the subsurface. The proposed research addresses this fundamental problem by creating an optimal model identification scheme based on available data for natural geologic formations and subsequently making the resulting software open source.