Predicting the Mpemba effect using machine learning.

Area of Science:

• Thermodynamics
• Statistical Mechanics
• Machine Learning

Background:

• The Mpemba effect, where warmer water can freeze faster than colder water, is a counterintuitive phenomenon.
• Studying the Mpemba effect within nonequilibrium thermodynamics and Markovian dynamics provides a theoretical framework.
• The Ising model serves as a relevant system for observing Markovian Mpemba effects.

Purpose of the Study:

• To investigate the predictability of the Markovian Mpemba effect in the Ising model using machine learning.
• To compare the accuracy of various machine learning algorithms in predicting this thermodynamic phenomenon.
• To explore the extrapolation capabilities of machine learning models trained on Mpemba effect data.

Main Methods:

• Application of machine learning algorithms: decision tree, neural networks, linear regression, and LASSO regression.
• Training and testing models on data from the Ising model exhibiting Markovian dynamics.
• Analysis of model performance, including positive and negative accuracy and extrapolation capabilities.

Main Results:

• Machine learning methods successfully predict the Mpemba effect in the Ising model.
• Models demonstrate accurate extrapolation to data outside their training range.
• Neural networks can predict the Mpemba effect even when trained solely on data where it is absent.
• Neural networks correctly predict the absence of the Mpemba effect for ferromagnetic interactions (positive J) when trained on antiferromagnetic data (negative J).

Conclusions:

• Machine learning offers a powerful tool for predicting the Mpemba effect in complex systems.
• The predictive capabilities extend beyond the training data, revealing underlying patterns.
• This approach bypasses the need for computationally intensive eigenvector calculations.