[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-120691-en":3,"doc-seo-120691-105":29,"detail-sidebar-cat-0-en-105":90},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":11,"language":21,"language_code":22,"site_id":23,"html_lang":22,"table_of_contents":24,"faqs":25,"seo_title":26,"seo_description":14,"update_tm":27,"read_time":28},120691,687197100911,"Himbo","https://ap-avatar.wpscdn.com/avatar/a000239b6f1da00475?x-image-process=image/resize,m_fixed,w_180,h_180&k=1785132997149421697",8,"Research & Report","Unsupervised machine learning for identifying phase transition using two-times clustering","Unsupervised learning is developed to identify phase transitions by extracting robust “perfect configurations” from degenerate samples through a two-times clustering strategy. The method assigns labels without prior knowledge, then trains a neural network to classify phases. Phase-transition points are located by inspecting derivatives of the predicted classification on the phase diagram. Validation on Ising, Potts, and Blume-Capel models shows that ordered configurations from two-times clustering enable accurate phase-diagram construction and reduce mislabeling of degenerate ordered states.","arXiv :2305 . 17687v1 [ cond-mat .dis-nn] 28 May 2023  \nUnsupervised machine learning for identifying phase transition using two-times clustering  \nNan Wu,1, 2 Zhuohan Li,3 and Wanzhou Zhang1, 4, ∗  \n1 College of Physics, Taiyuan University of Technology, Shanxi 030024, China  \n2 School for Physical Sciences, University of Science and Technology of China, Hefei 230026, China  \n3 College of Software, Taiyuan University of Technology, Shanxi 030024, China  \n4Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics,  \nUniversity of Science and Technology of China, Hefei 230026, China  \nIn recent years, developing unsupervised machine learning for identifying phase transition is a research direction. In this paper, we introduce a two-times clustering method that can help select perfect configurations from a set of degenerate samples and assign the configuration with labels in a manner of unsupervised machine learning. These perfect configurations can then be used to train a neural network to classify phases. The derivatives of the predicted classification in the phase diagram, show peaks at the phase transition points. The effectiveness of our method is tested for the Ising, Potts, and Blume-Capel models. By using the ordered configuration from two-times clustering, our method can provide a useful way to obtain phase diagrams.  \nI. INTRODUCTION  \nSince the pioneering work of J. Carrasquilla and R. G. Melko on applying machine learning (ML) methods to study spin systems [1], predicting the phase diagrams of interacting spin systems using ML has become an area of research interest [2] . Unsupervised ML methods are particularly useful in predicting phase diagrams as they do not require prior knowledge of the data labels. Common unsupervised ML methods include principal component analysis [3–5], t-distributed stochastic neighbor embedding [6, 7], diffusion maps [8–11], the confusion method [12], the active contour model (snake model) [13, 14], Calinski-Harabaz index[15, 16], and many others. Various indicators always signal atthe phase transition point.  \nSometimes, unsupervised methods incorporate certain steps of supervised learning. For example, the confusion method [12] determines labels to train the neural network (NN) based on guessed phase transition points. The best-guessed transition point is then determined based on the performance (accuracy) of the NN. In the NN-based snake model [13, 14], the learning network in the NN also needs tobe trained by data and dynamical labels while cooperating with the other guessing network.  \nIn contrast, Refs. [17] applied theoretical ground state configurations in the ordered phase as the training set to train the neural network without using real data, and the method was found to be effective for the Potts model. D.-R. Tan and F.-J. Jiang [18] even used datasets with only 0’s and 1’s to train the network and predict the critical points of the XY model and the O(3) model. Indeed, the identification of ordered phases is crucial for predicting phase transitions accurately.  \n In this paper, we propose a two-times clustering  \n∗ Correspoinding author: [zhangwanzhou@tyut.edu.cn](zhangwanzhou@tyut.edu.cn)  \nmethod to identify ordered configurations and their corresponding labels from numerical simulations. In the first clustering step, we select representative configurations from each physical parameter point. In the second clustering step, we obtain perfect configurationsand their corresponding labels. These selected perfected configurations and labels are then used to train the neural network, and the neural network is tested with real simulated data and mapped to a phase diagram.  \nThe reason for performing the second clustering step is to prevent the neural network from misidentifying degenerate states as belonging to different phases. For example, this step of clustering avoids treating the ordered state configurations of the four lattice sites Isin","cbCaiqu7kz1cwXtx","https://ap.wps.com/l/cbCaiqu7kz1cwXtx","pdf",1650664,1,"English","en",105,"# Introduction\n## Related unsupervised and semi-supervised approaches\n## Proposed two-times clustering framework\n## Clustering strategy and label assignment\n## Hamiltonian and model setup","[{\"question\":\"What is the two-times clustering method used for?\",\"answer\":\"It selects representative “perfect configurations” from degenerate numerical samples in two stages, producing configurations with consistent labels for training a neural network to classify phases.\"},{\"question\":\"How does the approach locate phase transition points?\",\"answer\":\"After the neural network predicts phase labels across the phase diagram, the derivatives of the predicted classification exhibit peaks at phase transition points.\"},{\"question\":\"Why is a second clustering step necessary?\",\"answer\":\"The second clustering prevents degenerate ordered states from being wrongly assigned to different phases, e.g., avoiding treating symmetry-related configurations as separate phases.\"}]","Unsupervised machine learning for identifying phase transition using two-times clustering | 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is the two-times clustering method used for?","Question",{"text":74,"@type":75},"It selects representative “perfect configurations” from degenerate numerical samples in two stages, producing configurations with consistent labels for training a neural network to classify phases.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"How does the approach locate phase transition points?",{"text":79,"@type":75},"After the neural network predicts phase labels across the phase diagram, the derivatives of the predicted classification exhibit peaks at phase transition points.",{"name":81,"@type":72,"acceptedAnswer":82},"Why is a second clustering step necessary?",{"text":83,"@type":75},"The second clustering prevents degenerate ordered states from being wrongly assigned to different phases, e.g., avoiding treating symmetry-related configurations as separate 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