用于学习阶段和关键度的通用神经网络
A universal neural network for learning phases and criticalities
摘要：
构造了一个通用的有监督神经网络（NN），用于计算研究相变的实际实验的相关临界性。所建立的神经网络的有效性进行了检查，通过应用它来计算几个三维（3D）模型的临界立方晶格，包括经典的$O(3)$模型，五态铁磁Potts模型，和二聚量子反铁磁海森堡模型。特别是，虽然所考虑的神经网络只训练一次一维（1D）晶格与120个网站，但它已经成功地确定了相关的临界点的研究3D系统。此外，在测试阶段不使用真实的状态配置。相反，所采用的配置的预测构建在120个站点的一维晶格上，并基于所考虑的模型的大量或微观状态。因此，我们的计算最终是有效的计算和所建立的神经网络的应用是非常广泛的。考虑到所研究的系统彼此之间差异很大，令人惊讶的是，这两种策略在训练和测试阶段的结合导致了一个高度通用的监督神经网络，用于学习3D模型的阶段和关键性。基于本研究中提出的结果，很可能可以为多体系统领域而不是临界现象构建更简单但更优雅的机器学习技术。
英文摘要：
A universal supervised neural network (NN) relevant to compute the associated criticalities of real experiments studying phase transitions is constructed. The validity of the built NN is examined by applying it to calculate the criticalities of several three-dimensional (3D) models on the cubic lattice, including the classical $O(3)$ model, the 5-state ferromagnetic Potts model, and a dimerized quantum antiferromagnetic Heisenberg model. Particularly, although the considered NN is only trained one time on a one-dimensional (1D) lattice with 120 sites, yet it has successfully determined the related critical points of the studied 3D systems. Moreover, real configurations of states are not used in the testing stage. Instead, the employed configurations for the prediction are constructed on a 1D lattice of 120 sites and are based on the bulk quantities or the microscopic states of the considered models. As a result, our calculations are ultimately efficient in computation and the applications of the built NN is extremely broaden. Considering the fact that the investigated systems vary dramatically from each other, it is amazing that the combination of these two strategies in the training and the testing stages lead to a highly universal supervised neural network for learning phases and criticalities of 3D models. Based on the outcomes presented in this study, it is favorably probable that much simpler but yet elegant machine learning techniques can be constructed for fields of many-body systems other than the critical phenomena.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
