[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-126564-en":3,"doc-seo-126564-105":30,"detail-sidebar-cat-0-en-105":92},{"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":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},126564,13056712833777,"Logic","https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0",8,"Research & Report","Unsupervised machine learning to classify the confinement of waves in periodic superstructures","A rigorous method classifies the dimensionality of wave confinement using unsupervised machine learning to improve an existing scaling approach. The study applies k-means++ and a model-based clustering algorithm to 3D superlattices of resonant cavities in a 3D inverse woodpile photonic band gap crystal across varied design parameters. Results are compared to each other and to direct scaling without clustering, with cluster validity indices used to infer required confinement dimensionalities. Highest accuracy comes from direct scaling followed by model-based refinement.","Research Article  \nVol. 31, No. 19/11 Sep 2023/Optics Express 31177  \nUnsupervised machine learning to classify the confinement of waves in periodic superstructures  \nMAREK KOZOˇN , 1,2,3  RUTGER SCHRIJVER , 2 MATTHIAS SCHLOTTBOM , 2  JAAP J. W. VAN DER VEGT, 2 AND WILLEM L. VOS1,*   \n1 Complex Photonic Systems (COPS), MESA + Institute for Nanotechnology, University of Twente, P.O. Box  \n217, 7500 AE Enschede, The Netherlands  \n2 Mathematics of Computational Science (MACS), MESA + Institute for Nanotechnology, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands  \n3 Current address: Pixel Photonics GmbH, Heisenbergstraße 11, 48149 Münster, Germany  \n*  \n[w.l.vos@utwente.nl](w.l.vos@utwente.nl)  \nAbstract: We propose a rigorous method to classify the dimensionality of wave confinement by utilizing unsupervised machine learning to enhance the accuracy of our recently presented scaling method [Phys. Rev. Lett. 129, 176401 (2022)] . We apply the standard k-means++ algorithm as well as our own model-based algorithm to 3D superlattices of resonant cavities embedded in a 3D inverse woodpile photonic band gap crystal with a range of design parameters. We compare their results against each other and against the direct usage of the scaling method without clustering. Since the clustering algorithms require the set of confinement dimensionalities present in the system as an input, we investigate cluster validity indices (CVIs) as a means to find these values. We conclude that the most accurate outcome is obtained by first applying direct scaling to find the correct set of confinement dimensionalities, and subsequently utilizing our model-based clustering algorithm to refine the results.  \n© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement  \n1. Introduction  \nCompletely controlling the propagation of photonic waves in periodic media is a key challenge that is essential for a large variety of applications [1–9] . A remarkable degree of control is obtained when confining waves by introducing disorder and functional defects into an otherwise periodic medium [10–13] . The interference of waves in such an altered structure may result in a strong concentration of the energy density inside a small sub-volume of the medium. Wave confinement has been investigated for different types of waves and in various settings, e.g., classical mechanics [14], photonics [3,4, 15–17], solid state physics [18–22], or magnonics [23,24] . Its applications include sensors, controlled spontaneous emission, and enhanced interactions between hybrid wave-types such as sound and light [25–33] .  \nRecently, we described a rigorous method to characterize the confinement of waves in periodic media with defects and in superlattices in general [34] . We first introduced a so-called confinement dimensionality, that quantifies the intuitive term of \"confinement\". Next we developed a scaling theory to determine the confinement dimensionality of every band in a given system. This scaling theory is valid for any type of physical wave-acoustic, electromagnetic, electron, spin, etc. -in both quantum and classical setting, and for systems in any dimension, and is readily usable in computer algorithms, allowing for automated classification of the bands.  \nNevertheless, the theory of Ref. [34] requires for every investigated superlattice a smaller reference superlattice, so that one can observe the scaling behavior of the key quantities when changing the supercell size. Generally, obtaining the data for the reference supercell is significantly  \n\\#492014 [https://doi.org/10.1364/OE.492014](https://doi.org/10.1364/OE.492014)  \nJournal © 2023 Received 30 Mar 2023; revised 31 May 2023; accepted 4 Jun 2023; published 6 Sep 2023  \nResearch Article  \nVol. 31, No. 19/11 Sep 2023/Optics Express 31178  \nless computationally demanding than performing the calculations for the supercell of interest. On the other hand, the requirement for ","cbCaiaJx2HPWXOBU","https://ap.wps.com/l/cbCaiaJx2HPWXOBU","pdf",5499451,1,23,"English","en",105,"# Abstract\n# Introduction\n## Background and motivation\n## Confinement dimensionality and scaling theory\n## Limitations of reference supercells\n## Clustering and unsupervised learning approach\n# Method overview (from introduction)","[{\"question\":\"What problem does the paper address about wave confinement?\",\"answer\":\"It targets accurate classification of the dimensionality of wave confinement in periodic superstructures, where waves localize due to defects or structured modifications.\"},{\"question\":\"Which unsupervised clustering methods are evaluated?\",\"answer\":\"The paper compares standard k-means++ clustering with a model-based clustering algorithm tailored to the confinement identification task.\"},{\"question\":\"How do the authors decide which confinement dimensionalities are present?\",\"answer\":\"They investigate cluster validity indices (CVIs) to estimate the set of confinement dimensionalities needed as input for clustering.\"}]","Unsupervised machine learning to classify the confinement of waves in periodic superstructures | 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problem does the paper address about wave confinement?","Question",{"text":76,"@type":77},"It targets accurate classification of the dimensionality of wave confinement in periodic superstructures, where waves localize due to defects or structured modifications.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"Which unsupervised clustering methods are evaluated?",{"text":81,"@type":77},"The paper compares standard k-means++ clustering with a model-based clustering algorithm tailored to the confinement identification task.",{"name":83,"@type":74,"acceptedAnswer":84},"How do the authors decide which confinement dimensionalities are present?",{"text":85,"@type":77},"They investigate cluster validity indices (CVIs) to estimate the set of confinement dimensionalities needed as input for 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