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

翻译：本文提出了一种基于物理信息的深度学习方法，用于预测复制者方程，从而实现对种群动态的精确预测。这一方法创新使我们能够为缺乏显式数学模型的系统推导出控制微分方程或差分方程。我们采用了由Fasel、Kaiser、Kutz、Brunton和Brunt于2016年首次提出的SINDy模型来获取复制者方程，这将显著推进我们对进化生物学、经济系统和社会动态的理解。通过改进生态学、社会结构和道德行为等多学科的预测模型，我们的研究为动态系统中塑造进化结果的变量间复杂相互作用提供了新的见解。