Andriushchenko Petr, Kapitan Dmitrii, Kapitan Vitalii
National Center for Cognitive Research, ITMO University, bldg. A, Kronverksky Pr. 49, 197101 Saint Petersburg, Russia.
Department of Theoretical Physics and Smart Technologies, Far Eastern Federal University, Russky Island, 10 Ajax Bay, 690922 Vladivostok, Russia.
Entropy (Basel). 2022 May 14;24(5):697. doi: 10.3390/e24050697.
Spin glass is the simplest disordered system that preserves the full range of complex collective behavior of interacting frustrating elements. In the paper, we propose a novel approach for calculating the values of thermodynamic averages of the frustrated spin glass model using custom deep neural networks. The spin glass system was considered as a specific weighted graph whose spatial distribution of the edges values determines the fundamental characteristics of the system. Special neural network architectures that mimic the structure of spin lattices have been proposed, which has increased the speed of learning and the accuracy of the predictions compared to the basic solution of fully connected neural networks. At the same time, the use of trained neural networks can reduce simulation time by orders of magnitude compared to other classical methods. The validity of the results is confirmed by comparison with numerical simulation with the replica-exchange Monte Carlo method.
自旋玻璃是最简单的无序系统，它保留了相互作用的受挫元素的全部复杂集体行为范围。在本文中，我们提出了一种使用定制深度神经网络计算受挫自旋玻璃模型热力学平均值的新方法。自旋玻璃系统被视为一个特定的加权图，其边值的空间分布决定了系统的基本特征。已经提出了模仿自旋晶格结构的特殊神经网络架构，与全连接神经网络的基本解决方案相比，这提高了学习速度和预测准确性。同时，与其他经典方法相比，使用经过训练的神经网络可以将模拟时间减少几个数量级。通过与复制交换蒙特卡罗方法的数值模拟进行比较，证实了结果的有效性。
