将基于范数的空间表示转换为基于图的时空流行病学模型空间表示
Transforming Norm-based To Graph-based Spatial Representation for Spatio-Temporal Epidemiological Models
AI总结：
针对时空流行病学模型，本文提出将基于范数的空间表示近似转换为基于图表示的框架，结合智能体模拟与启发式优化，在三个真实案例中平均保留94%的准确性。
摘要：
大流行病具有深远的社会和经济影响，对全球健康、死亡率、经济稳定和政治格局构成重大威胁。为应对这些挑战，大量研究采用时空模型来增进我们对这些复杂现象的理解和管理。这些时空模型大致可分为两大空间类别：基于范数的模型和基于图的模型。基于范数的模型通常更准确、更易于建模，但计算量更大，且需要更多数据进行拟合。另一方面，基于图的模型准确性较低、建模难度较大，但计算量较小，拟合所需数据也更少。因此，理想情况下，人们希望使用基于图的模型，同时保留基于范数的模型所获得的表示准确性。在本研究中，我们探索了针对这些模型从基于范数的空间表示转换为基于图的空间表示的能力。我们首先证明两者之间不存在解析映射，因此需要改用近似数值方法。我们为这一任务引入了一个新颖框架，并给出了使用多种启发式优化方法的十二种可能实现。研究结果表明，通过利用基于智能体的模拟和启发式算法来近似图节点位置以及人群的空间行走动力学，人们可以使用基于图的空间表示，而不会过多损失模型的准确性和表达能力。我们在三个真实案例中研究了该框架，平均实现了94%的准确性保留。此外，对合成案例的分析表明，所提出框架对空间和时间属性的变化都具有相对稳健性。
英文摘要：
Pandemics, with their profound societal and economic impacts, pose significant threats to global health, mortality rates, economic stability, and political landscapes. In response to these challenges, numerous studies have employed spatio-temporal models to enhance our understanding and management of these complex phenomena. These spatio-temporal models can be roughly divided into two main spatial categories: norm-based and graph-based. Norm-based models are usually more accurate and easier to model but are more computationally intensive and require more data to fit. On the other hand, graph-based models are less accurate and harder to model but are less computationally intensive and require fewer data to fit. As such, ideally, one would like to use a graph-based model while preserving the representation accuracy obtained by the norm-based model. In this study, we explore the ability to transform from norm-based to graph-based spatial representation for these models. We first show no analytical mapping between the two exists, requiring one to use approximation numerical methods instead. We introduce a novel framework for this task together with twelve possible implementations using a wide range of heuristic optimization approaches. Our findings show that by leveraging agent-based simulations and heuristic algorithms for the graph node's location and population's spatial walk dynamics approximation one can use graph-based spatial representation without losing much of the model's accuracy and expressiveness. We investigate our framework for three real-world cases, achieving 94\% accuracy preservation, on average. Moreover, an analysis of synthetic cases shows the proposed framework is relatively robust for changes in both spatial and temporal properties.
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