Laboratory of Dynamics in Biological Systems, Department of Cellular and Molecular Medicine, KU Leuven, Leuven 3000, Belgium.
Chair of Fluid Systems, TU Darmstadt, 64287 Darmstadt, Germany.
Phys Rev E. 2023 Jun;107(6-1):064305. doi: 10.1103/PhysRevE.107.064305.
The rapid increase of population and settlement structures in the Global South during recent decades has motivated the development of suitable models to describe their formation and evolution. Such settlement formation has been previously suggested to be dynamically driven by simple pattern-forming mechanisms. Here, we explore the use of a data-driven white-box approach, called SINDy, to discover differential equation models directly from available spatiotemporal demographic data for three representative regions of the Global South. We show that the current resolution and observation time of the available data are insufficient to uncover relevant pattern-forming mechanisms in settlement development. Using synthetic data generated with a generic pattern-forming model, the Allen-Cahn equation, we characterize what the requirements are for spatial and temporal resolution, as well as observation time, to successfully identify possible model system equations. Overall, the study provides a theoretical framework for the analysis of large-scale geographical and/or ecological systems, and it motivates further improvements in optimization approaches and data collection.
在最近几十年，全球南方的人口和定居点结构迅速增加，这促使人们开发出合适的模型来描述它们的形成和演变。先前有人提出，这种定居点的形成是由简单的模式形成机制动态驱动的。在这里，我们探索了使用一种数据驱动的白盒方法（称为 SINDy），直接从全球南方三个有代表性地区的现有时空人口数据中发现微分方程模型。我们表明，当前可用数据的分辨率和观测时间不足以揭示定居点发展中相关的模式形成机制。我们使用具有通用模式形成模型（Allen-Cahn 方程）生成的合成数据，来描述成功识别可能的模型系统方程所需的空间和时间分辨率以及观测时间的要求。总的来说，该研究为分析大规模地理和/或生态系统提供了理论框架，并促使优化方法和数据收集得到进一步改进。
