Amorim Felipe, Wisely Joey, Buckley Nathan, DiNardo Christiana, Sadasivan Daniel
Ave Maria University, Ave Maria, Florida 34142, USA.
Phys Rev E. 2023 Aug;108(2-1):024137. doi: 10.1103/PhysRevE.108.024137.
The Mpemba effect can be studied with Markovian dynamics in a nonequilibrium 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 nonlinear regression with the least absolute shrinkage and selection operator (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 in 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 antiferromagnetic 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.
可以在非平衡热力学框架下，用马尔可夫动力学研究姆潘巴效应。在包括伊辛模型在内的各种系统中都能观察到马尔可夫姆潘巴效应。我们证明，使用几种机器学习方法，即决策树算法、神经网络、线性回归以及采用最小绝对收缩和选择算子（LASSO）方法的非线性回归，可在伊辛模型中预测马尔可夫姆潘巴效应。比较了这些方法的正、负准确率。此外，我们发现机器学习方法可用于准确外推到其训练范围之外的数据。当仅在未出现姆潘巴效应的数据上进行训练时，神经网络甚至可以预测姆潘巴效应的存在。这表明，在未出现该结果的系数中包含了哪些系数会导致姆潘巴效应的信息。此外，即使仅在对应反铁磁伊辛模型的负J值上进行训练，神经网络也能预测对于对应铁磁伊辛模型的正J值，姆潘巴效应不会出现。所有这些结果表明，无需明确计算特征向量，就能在复杂且计算成本高昂的系统中预测姆潘巴效应。
