用深度学习预测进化博弈中的种群动态，无需事先知道方程。
Deep learning approach for predicting the replicator equation in evolutionary game theory
- 结合物理信息与深度学习，从数据中推导出复制者方程。
- 在无明确数学模型时仍能准确预测系统演化趋势。
- 适用于生态、经济、社会行为等复杂系统的演化分析。
本文提出一种物理信息深度学习方法，用于预测进化博弈论中的复制者方程，实现对种群动态的精准预测。该方法创新性地采用Fasel等人（2016a）提出的SINDy模型，从数据中推导出系统对应的微分或差分方程，即使在缺乏显式数学模型的情况下也能有效建模。本研究显著提升了对进化生物学、经济系统及社会动态的理解，为生态、社会结构和道德行为等多领域提供了新的建模视角，揭示了动态系统中变量相互作用对演化结果的影响。
原文摘要 · Abstract (English)
This paper presents a physics-informed deep learning approach for predicting the replicator equation, allowing accurate forecasting of population dynamics. This methodological innovation allows us to derive governing differential or difference equations for systems that lack explicit mathematical models. We used the SINDy model first introduced by Fasel, Kaiser, Kutz, Brunton, and Brunt 2016a to get the replicator equation, which will significantly advance our understanding of evolutionary biology, economic systems, and social dynamics. By refining predictive models across multiple disciplines, including ecology, social structures, and moral behaviours, our work offers new insights into the complex interplay of variables shaping evolutionary outcomes in dynamic systems
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