机器学习在座逾渗相变问题中的应用

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摘要：

机器学习理论区别于传统方法,因其在对于复杂的数据集识别、分类的准确性和高效性而被广泛应用于各个领域.识别相变是机器学习和统计物理领域相结合的最有代表性的工作.到目前为止,机器学习完成的相变识别几乎都是基于具有动力学演化过程的自旋模型,如Ising模型等,而其在另一类不具有动力学演化过程而完全由系统结构特征决定的相变模型,如逾渗模型等,仍未有细致研究.本文结合现有的机器学习技术,卷积神经网络和一般向量机,对二维方格子上的座逾渗问题进行了研究,发现能以高正确率对不同相的构型进行识别,证明了机器学习在这类问题上研究的可行性.通过已完成训练的学习机对不同参数下构型预测的正确率计算,发现正确率在相变点附近会出现急剧衰减,与系统参数呈幂律衰减.这与传统相变理论一致.通过定量计算,还发现2种学习机的正确率衰减规律都满足同一个幂律指数.这不仅进一步从全新的角度揭示了相变的普适性,而且为找寻相变点提供了新的方法.

Different from traditional physical approaches,machine learning technics are widely applied in various fields benefitted from their high accuracy and efficiency in detection and classification of complex data sets.Identifying phase transitions are the most typical works in the field of combination of machine learning and statistical physics.So far,researches are mainly focused on the spin models with dynamical evolutions,such as Ising model.However,a more general type of phase transition models,such as the percolation model,which is not determined by dynamical evolutions but the intrinsic property of itself,has not been researched yet.In this article,combined with the new machine learning methods,the convolutional neural network and the general vector machine,we study the two-dimensional square-lattice site percolation model.We find that well-designed networks can identify different configurations with a high accuracy,which proves that machine learning works on this problem.Then,by calculating accuracies of our networks for identifying configurations on different parameters,we find the accuracy drops near the critical point in both models,and this decay follows the power-law with the parameter,which is corresponding to the traditional phase transition theory.We calculated the exponents of the power-law and find the exponents are nearly the same in both different models.Our research does not only reveal the universality of phase transitions,but also provides a new way to find the critical point.

作者：

徐荣幸赵鸿

Xu Rongxing;Zhao Hong(Department of Physics,Xiamen University,Xiamen 361005,China)

机构地区：

厦门大学物理系

出处:

《betway官方app 学报：自然科学版》 CAS 北大核心 2019年第1期45-51,共7页

基金:

国家自然科学基金重点项目(11335006)

关键词:

机器学习卷积神经网络一般向量机座逾渗相变正确率标度关系

machine learning convolutional neural network general vector machine site percolation phase transition accuracy scaling relation