人工神經網路在物理上的應用：二維正方形晶格上Potts model 相變之研究

Abstract

這篇論文主要探討了卷積神經網路(convolutional neural network)在二維正方形晶格上的Potts model之應用。我們使用卷積神經網路對蒙地卡羅演算法模擬出的自旋狀態加以分析。不同於相關文獻中常用的方法，在本次研究中，我們使用低溫有序相中的自旋狀態作為訓練集，並以輸出向量O ⃗之長度R做為主要觀測量。藉由此方法，我們得到了和已知文獻上一致的結果。此方法減少了以人工神經網路研究凝態模型時所耗費的計算資源。使用此方式訓練出的卷積神經網路除了可以偵測臨界溫度T_c外，亦可用來辨識相變的類型為一階或二階。This thesis mainly discusses the application of convolutional neural network to the Potts model on the two-dimensional square lattice. We use the constructed convolution neural network to analyze the spin configurations which were obtained by the Monte-Carlo simulations. Our method is different from those used in the related literature. Here, the spin configurations in the ordered phase are empolyed as the training set. In addition, the norm of the output vectors R is considered as the main observable. With this method, our determined results are consistent with the known ones in the literature. This method dramatically reduces the computational resources needed to study the condensed matter systems using the artificial neural network. Apart from detecting the critical temperature T_c, the convolution neural network built in our study can also be used to identify the nature of phase transition, namely whether they are first order or second order.