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研究生: 李建德
Li, Chien-De
論文名稱: 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
Applications of artificial neural networks in physics : a study of the phase transitions of two dimensional Potts models on the quare lattice
指導教授: 江府峻
Jiang, Fu-Jiun
學位類別: 博士
Doctor
系所名稱: 物理學系
Department of Physics
論文出版年: 2018
畢業學年度: 107
語文別: 中文
論文頁數: 44
中文關鍵詞: 蒙地卡羅模擬相變Potts model人工神經網路
英文關鍵詞: Monte Carlo simulations, Potts model, phase transition, artificial neural network
DOI URL: http://doi.org/10.6345/DIS.NTNU.DP.022.2018.B04
論文種類: 學術論文
相關次數: 點閱:198下載:50
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  • 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.

    摘要 i Abstract ii Chapter 1 導論 1 Chapter 2 模型 4 Chapter 3 研究方法 8 蒙地卡羅方法 9 Metropolis 演算法 14 Metropolis 演算法 15 學習 17 獨熱編碼 19 人工神經網路 21 多層感知器 26 卷積神經網路 28 資料集與觀測量|R| 31 直方圖方法 33 Chapter 4 數值結果 34 蒙地卡羅方法之數值結果 34 卷積神經網路之數值結果 36 Chapter 5 討論 38 附錄 40 參考文獻 42

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