[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-124925-en":3,"doc-seo-124925-105":30,"detail-sidebar-cat-0-en-105":83},{"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":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},124925,5909877438554,"Maeve","https://ap-avatar.wpscdn.com/avatar/5600025385ad2bf12a7?_k=1778553567797529272",8,"Research & Report","An inversion problem for optical spectrum data via physics-guided machine learning","The work proposes the regularized recurrent inference machine (rRIM) to address an inverse problem: extracting the pairing glue function from experimentally measured optical spectra. By embedding physical principles into both training and inference, rRIM improves noise robustness, handles out-of-distribution data more flexibly, and reduces the amount of required data. The method reliably recovers pairing glue functions from experimental spectra and produces promising solutions for related ill-posed inverse problems formulated as Fredholm integral equations of the first kind.","An inversion problem for optical spectrum data via physics-guided machine learning.  \narXiv:2404.02387v1 [[physics.data-an](physics.data-an)] 3 Apr 2024  \nHwiwoo Park 1 , Jun H. Park2 ,†, and Jungseek Hwang 1 ,∗  \n1 Department of Physics, Sungkyunkwan University, Suwon, Gyeonggi-do 16419, Republic of Korea  \n2 School of Mechanical Engineering, Sungkyunkwan University, Suwon, Gyeonggi-do 16419, Republic of Korea  \n(Dated: April 4, 2024)  \nAbstract  \nWe propose the regularized recurrent inference machine (rRIM), a novel machine-learning approach to solve the challenging problem of deriving the pairing glue function from measured optical spectra. The rRIM incorporates physical principles into both training and inference and affords noise robustness, flexibility with out-of-distribution data, and reduced data requirements. It effectively obtains reliable pairing glue functions from experimental optical spectra and yields promising solutions for similar inverse problems of the Fredholm integral equation of the first kind.  \nCorrespondence to [emails:†[jun.park@skku.edu](jun.park@skku.edu) and∗[jungseek@skku.edu](jungseek@skku.edu)] .  \nI. INTRODUCTION  \nExperimental and theoretical investigations on high-temperature copper-oxide (cuprate) superconductors, since their discovery over 35 years ago [1, 2], have afforded extensive results [3] . Despite these efforts, the microscopic electron-electron pairing mechanism for superconductivity remains elusive. In this regard, researchers have adopted innovative experimental techniques. Particularly, optical spectroscopy has the potential to elucidate the aforementioned pairing mechanisms because it is the only spectroscopic experimental method capable of providing quantitative physical quantities. The absolute pairing glue spectrum measured via optical spectroscopy may serve as a “smoking gun” evidence to address for this problem. The measured spectrum entails information concerning the pairing glue responsible for superconductivity. Extracting this glue function from the measured optical spectra via the decoding approach, which involves an inverse problem, contributes an essential aspect to the elucidation of high-temperature superconductivity.  \nThe decoding-related inversion problem concerning physical systems is expressed as follows:  \nτop~~ ~~(1ω,~~ ~~T) = Z0 ∞ dΩI2 χ(Ω, T) K (ω,Ω, T) , (1)  \nwhich is referred to as the generalized Allen formula [4–7] . Here 1/τop (ω) is the optical scattering rate, K(ω,Ω) is the kernel, and I2 χ (ω) is the pairing glue function, which describes interacting electrons by exchanging the force-mediating boson. Further, χ (ω) is the boson  \nspectrum and I denotes the electron–boson coupling constant. The kernel is given as  \nK (ω,Ω, T) =πω 􀀔 2ω coth 􀀒 Ω2T􀀓− (ω + Ω)coth 􀀒 ω~~ ~~+2TΩ 􀀓  \n(2)  \n+(ω − Ω)coth 􀀒 ω~~ ~~−2TΩ 􀀓􀀕 .  \nThis is referred to as the Shulga kernel [5] . The goal was to infer the glue function from the optical scattering rate obtained using optical spectroscopy [7] . Eq. (1) can be expressed ina more general form as follows:  \ny (t) = Zab dτ x (τ) k (t,τ) , (3)  \nwhich is the Fredholm integral equation of the first kind. Here, k (t,τ) is referred to as the kernel and determined by the underlying physics of the given problem, and x (τ) and y (t) are physical quantities related to each other through the integral equation. Such inverse problems occur in many areas of physics [6, 8, 9] and are known to be ill-posed [10] . The ill-posed nature arises from the instability of solutions in Eq. (3), where small changes in y can lead to significant changes in x. Consequently, obtaining a solution to the inverse problem becomes challenging, particularly when observations are corrupted by noise.  \nConventional approaches for solving inverse problems, expressed in the form of Eq. (3) include singular value decomposition (SVD) [11], least squares fit [12, 13], maximum entropy method (MEM) [6, 7], and Tikhonov regularization [14] . In particular, the MEM ","cbCaikQuYABd8ALz","https://ap.wps.com/l/cbCaikQuYABd8ALz","pdf",526406,1,19,"English","en",105,"# Introduction\n## Inverse problems in optical spectroscopy\n## Fredholm integral equation of the first kind\n## Conventional regularization methods\n## Physics-guided machine learning for inverse problems","[{\"question\":\"Why is the inversion problem challenging?\",\"answer\":\"Because it is ill-posed: small changes in measured data can lead to large, unstable changes in the inferred function, especially under noise.\"}]","An inversion problem for optical spectrum data via physics-guided machine learning | PDF",1785895420,48,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":78,"head_meta":80,"extra_data":82,"updated_unix":28},"an-inversion-problem-for-optical-spectrum-data-via-physics-guided-machine-learning","",{"@graph":36,"@context":77},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/an-inversion-problem-for-optical-spectrum-data-via-physics-guided-machine-learning/124925/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-05",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71],{"name":72,"@type":73,"acceptedAnswer":74},"Why is the inversion problem challenging?","Question",{"text":75,"@type":76},"Because it is ill-posed: small changes in measured data can lead to large, unstable changes in the inferred function, especially under noise.","Answer","https://schema.org",{"og:url":52,"og:type":79,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":81,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":84},[85,89,93,97,102,107,112,115,120,123,127],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":86,"show_sort_weight":87,"slug":88},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":90,"show_sort_weight":91,"slug":92},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Exam",70,"exam",{"id":98,"doc_module":4,"doc_module_name":46,"category_name":99,"show_sort_weight":100,"slug":101},5,"Comic",60,"comic",{"id":103,"doc_module":4,"doc_module_name":46,"category_name":104,"show_sort_weight":105,"slug":106},6,"Technology",50,"technology",{"id":108,"doc_module":4,"doc_module_name":46,"category_name":109,"show_sort_weight":110,"slug":111},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":113,"slug":114},30,"research-report",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},9,"Religion & Spirituality",20,"religion-spirituality",{"id":118,"doc_module":4,"doc_module_name":46,"category_name":121,"show_sort_weight":118,"slug":122},"World Cup","world-cup",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":124,"slug":126},10,"Lifestyle","lifestyle",{"id":21,"doc_module":4,"doc_module_name":46,"category_name":128,"show_sort_weight":98,"slug":129},"General","general"]