论文标题
神经网络方法的缩放分析临界现象分析
Neural Network Approach to Scaling Analysis of Critical Phenomena
论文作者
论文摘要
确定表现出关键现象的系统的通用类别是物理学的核心问题之一。从数据中确定此通用类别类别有几种方法。随着在缩放函数上执行崩溃图的方法，已经提出了多项式回归，而多项式回归较少，而高斯过程回归（具有很高的精度和灵活性，但在计算上很重）。在本文中，我们提出了使用神经网络的回归方法。计算复杂性仅在数据点数中线性。我们证明了对二维ISING模型和键渗透问题的临界现象有限尺寸缩放分析的建议方法，以确认性能。在两种情况下，此方法都有效地获得了临界值的准确性。
Determining the universality class of a system exhibiting critical phenomena is one of the central problems in physics. There are several methods to determine this universality class from data. As methods performing collapse plots onto scaling functions, polynomial regression, which is less accurate, and Gaussian process regression, which provides high accuracy and flexibility but is computationally heavy, have been proposed. In this paper, we propose a regression method using a neural network. The computational complexity is only linear in the number of data points. We demonstrate the proposed method for the finite-size scaling analysis of critical phenomena on the two-dimensional Ising model and bond percolation problem to confirm the performance. This method efficiently obtains the critical values with accuracy in both cases.
