Transforming Norm-based To Graph-based Spatial Representation for Spatio-Temporal Epidemiological Models

2024-02-22

arXiv.org

AI Summary

In epidemic modeling, norm-based and graph-based spatial representations face a fundamental trade-off between accuracy and computational efficiency, with no analytical mapping existing between them. Method: This paper proposes the first learnable numerical approximation framework for cross-paradigm spatial representation conversion. Grounded in theoretical proof of the absence of closed-form mappings, we design a unified framework integrating 12 heuristic optimization variants, surrogate simulation, spatial random-walk dynamics modeling, and graph neural network-compatible embeddings. Contribution/Results: Evaluated on synthetic data and three real-world epidemic scenarios, our method preserves 94% of the original norm-based model’s accuracy—substantially outperforming baselines—while exhibiting strong robustness to spatiotemporal scale variations. It is the first approach enabling high-fidelity, differentiable, and low-data-dependent conversion between norm-based and graph-based spatial representations.

Technology Category

• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Graph-based Machine Learning

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding

Abstract

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.

Problem

• Transforming norm-based to graph-based spatial epidemic models
• Achieving computational efficiency without losing representation accuracy
• Developing approximation methods for spatial representation conversion

Innovation

• Transforming norm-based to graph-based spatial representation
• Using heuristic optimization approaches for approximation
• Leveraging agent-based simulations for accuracy preservation