Predicting the Mpemba Effect Using Machine Learning

TL;DR

This paper demonstrates that machine learning methods can effectively predict the Markovian Mpemba Effect in the Ising model, including extrapolation beyond training data and predicting effects in different parameter regimes.

Contribution

It introduces the use of various machine learning techniques to predict the Mpemba Effect in complex thermodynamic systems without explicit eigenvector calculations.

Findings

Machine learning methods accurately predict the Mpemba Effect in the Ising model.

Neural networks can extrapolate and predict the effect outside the training data range.

Models can predict the absence of the effect in certain parameter regimes even when trained elsewhere.

Abstract

The Mpemba Effect 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 positive and negative accuracy 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 which coefficients result in the Mpemba Effect is contained in coefficients where the results does not occur. Furthermore, neural networks can predict that the Mpemba effect does not occur for positive $J$, corresponding to the ferromagnetic ising model even when they are only trained on negative $J$, corresponding to the anti-ferromagnetic ising model. All of these results demonstrate that the Mpemba Effect can be predicted in complex, computationally expensive systems, without explicit calculations of the eigenvectors.