Predicting the Mpemba Effect Using Machine Learning

The Mpemba Effect -- when a system that is further from equilibrium relaxes faster than a system that is closer -- can be studied with Markovian dynamics in a non-equilibrium thermodynamics framework. The Markovian Mpemba Effect can be observed in a variety of systems including the Ising model. We demonstrate that the Markovian Mpemba Effect can be predicted in the Ising model with several machine learning methods: the decision tree algorithm, neural networks, linear regression, and non-linear regression with the LASSO method. The effectiveness of these methods are compared. Additionally, we find that machine learning methods can be used to accurately extrapolate to data outside the range which they were trained. Neural Networks can even predict the existence of the Mpemba Effect when they are trained only on data in which the Mpemba Effect does not occur. This indicates that information about the effect is contained even in systems where it is not present. All of these results demonstrate that the Mpemba Effect can be predicted in complex, computationally expensive systems, without performing full calculations.