Toward Eliminating the “Curse of Dimensionality” in Large-Scale Groundwater Modeling

In this paper, we present a nature-inspired, hierarchical patch dynamics paradigm for modeling complex groundwater systems across multiple scales – one that has the potential to substantially alleviate the infamous “curse of dimensionality” and the associated computational bottlenecks. The new modeling paradigm is inspired by the observations on how biological systems have been doing a great job coping with complexity, especially on their ability to process far more information than their limited bandwidths allow. Specifically, the new paradigm takes advantage of hierarchy theory, mimics how biological systems effectively “divide and conquer” complexities, and decouples scale-dependent dynamics hierarchically. The result is a systematic framework that enables modeling complex groundwater systems in high resolution without having to solve large, ill-posed matrix systems. We illustrate the effectiveness of the new hierarchical paradigm and its potential for large-scale groundwater modeling using an example.