Deep learning approach for predicting the replicator equation in evolutionary game theory
This work addresses the need for better predictive models in evolutionary game theory, with applications in ecology, social structures, and moral behaviors, though it builds on existing methods like SINDy, making it incremental.
The paper tackles the problem of predicting population dynamics in systems lacking explicit mathematical models by using a physics-informed deep learning approach to derive the replicator equation, achieving accurate forecasting that advances understanding in evolutionary biology, economics, and social dynamics.
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