Deep learning approach for predicting the replicator equation in evolutionary game theory

TL;DR

This paper introduces a physics-informed deep learning method to accurately predict the replicator equation, enabling better modeling of population dynamics in various complex systems without explicit mathematical models.

Contribution

It combines deep learning with the SINDy model to derive governing equations for systems lacking explicit models, advancing interdisciplinary understanding of evolutionary dynamics.

Findings

Successfully predicts population dynamics across disciplines

Enhances understanding of evolutionary and social systems

Provides a new tool for modeling complex adaptive systems

Abstract

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