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.

中文翻译：

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使用机器学习预测 Mpemba 效应

Mpemba 效应——当一个远离平衡的系统比一个更接近的系统松弛得更快——可以在非平衡热力学框架中用马尔可夫动力学研究。Markovian Mpemba 效应可以在包括 Ising 模型在内的各种系统中观察到。我们证明了马尔可夫 Mpemba 效应可以用几种机器学习方法在 Ising 模型中预测：决策树算法、神经网络、线性回归和使用 LASSO 方法的非线性回归。比较了这些方法的有效性。此外，我们发现机器学习方法可用于准确推断超出训练范围的数据。当神经网络仅在未发生 Mpemba 效应的数据上进行训练时，它们甚至可以预测 Mpemba 效应的存在。这表明即使在不存在效果的系统中也包含有关效果的信息。所有这些结果表明，可以在复杂、计算成本高昂的系统中预测 Mpemba 效应，而无需执行完整的计算。