[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-126171-en":3,"doc-seo-126171-105":31,"detail-sidebar-cat-0-en-105":93},{"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":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":28,"seo_description":14,"update_tm":29,"read_time":30},126171,3985741905716,"Rowan","https://ap-avatar.wpscdn.com/davatar_994ba38a5ba835b3df7d355c54d3ed8d",8,"Research & Report","QUOTIENT COMPLEX (QC)-BASED MACHINE LEARNING FOR 2D PEROVSKITE DESIGN - A PREPRINT","Two-dimensional (2D) halide layered perovskites offer strong stability and optoelectronic performance for photovoltaic technology, yet insufficient material representations hinder design and discovery. The work proposes a quotient complex (QC) computational topology framework for material representation, integrating QC-based features into learning models for 2D perovskite design. It introduces quotient complex descriptors derived from unit cells and periodic boundary conditions, jointly encoding higher-order interactions and periodicity. Benchmarked on the NMSE databank, QC-based machine learning models outperform prior methods and efficiently characterize structural attributes, highlighting periodicity as a key predictive factor.","QUOTIENT COMPLEX (QC)-BASED MACHINE LEARNING FOR 2D  \nPEROVSKITE DESIGN  \nA PREPRINT  \narXiv :2407 . 16996v 1 [ cs .CE] 24 Jul 2024  \nChuan-Shen Hu  \nDivision of Mathematical Sciences School of Physical and Mathematical Sciences Nanyang Technological University Singapore 637371 [chuanshen.hu@ntu.edu.sg](chuanshen.hu@ntu.edu.sg)  \nKelin Xia  \nDivision of Mathematical Sciences School of Physical and Mathematical Sciences Nanyang Technological University Singapore 637371 [xiakelin@ntu.edu.sg](xiakelin@ntu.edu.sg)  \nRishikanta Mayengbam  \nDivision of Physics & Applied Physics School of Physical and Mathematical Sciences Nanyang Technological University Singapore 637371 [rishikanta.m@ntu.edu.sg](rishikanta.m@ntu.edu.sg)  \nTze Chien Sum  \nDivision of Physics & Applied Physics School of Physical and Mathematical Sciences Nanyang Technological University Singapore 637371 [tzechien@ntu.edu.sg](tzechien@ntu.edu.sg)  \nJuly 29, 2024  \nABSTRACT  \nWith remarkable stability and exceptional optoelectronic properties, two-dimensional (2D) halide layered perovskites hold immense promise for revolutionizing photovoltaic technology. Presently, inadequate representations have substantially impeded the design and discovery of 2D perovskites. In this context, we introduce a novel computational topology framework termed the quotient complex (QC), which serves as the foundation for the material representation. Our QC-based features are seamlessly integrated with learning models for the advancement of 2D perovskite design. At the heart of this framework lies the quotient complex descriptors (QCDs), representing a quotient variation of simplicial complexes derived from materials unit cell and periodic boundary conditions. Differing from prior material representations, this approach encodes higher-order interactions and periodicity information simultaneously. Based on the well-established New Materials for Solar Energetics (NMSE) databank, our QC-based machine learning models exhibit superior performance against all existing counterparts. This underscores the paramount role of periodicity information in predicting material functionality, while also showcasing the remarkable efficiency of the QC-based model in characterizing materials structural attributes.  \nKeywords 2D perovskite · Material design · Quotient complex · Persistent homology  \nIntroduction  \nMaterials innovation and design stand at the forefront of humanity’s response to the grand challenge of achieving sustainable energy generation and combating climate change [2] . In less than a decade, perovskites have showcased remarkable power conversion efficiency (PCE), standing shoulder-to-shoulder with state-of-the-art technologies. The performance not only establishes them as a formidable contender but also hints at the possibility of a paradigm shift in photovoltaic (PV) technology [3, 4] . Especially, single-junction perovskite solar cells achieve an impressive 26% efficiency, while perovskite-silicon tandem counterparts reach an even higher 33%, outperforming single-junction silicon solar cells [5, 6] . In recent times, the advent of a diverse family of two-dimensional (2D) perovskites positions them as leading candidates for the next generation of perovskite materials. For instance, beyond the archetypal  \nA PREPRINT-JULY 29, 2024  \nFigure 1: Illustration of a crystal structure (Panel A) and its finite representations (Panel B), including the unit cell and supercell representations. The entire crystal structure is built by repeating the unit cell or supercell. In particular, the supercell depicted in B represents a 2 × 2 × 2 extension of the unit cell. Based on the periodicity of duplicated atoms, a quotient graph representation is obtained (Panel C) . Furthermore, by leveraging higher-dimensional objects (e.g., 2-dimensional surfaces) in the quotient graph, the quotient complex (Panel D) is established. Panel E illustrates a schematic image of a quotient complex filtration derived from the c","cbCaimIdM2fPkb9L","https://ap.wps.com/l/cbCaimIdM2fPkb9L","pdf",9662612,10,1,36,"English","en",105,"# Abstract\n# Introduction\n## Background and motivation for data-driven perovskite design\n## Key representation challenge in 2D perovskites\n## Proposed quotient complex (QC) framework and its purpose","[{\"question\":\"What problem does the paper address in designing 2D perovskites?\",\"answer\":\"It addresses the limitation of inadequate material representations, which slows down the design and discovery of 2D perovskites.\"},{\"question\":\"What is the quotient complex (QC) framework?\",\"answer\":\"The QC framework is a computational topology approach that provides a foundation for representing materials for downstream learning models.\"},{\"question\":\"How do QC-based machine learning models perform compared with existing methods?\",\"answer\":\"Using the NMSE databank, the QC-based models show superior performance against all existing counterparts, emphasizing the importance of periodicity information.\"}]","QUOTIENT COMPLEX (QC)-BASED MACHINE LEARNING FOR 2D PEROVSKITE DESIGN - A PREPRINT | PDF",1785903555,91,{"code":4,"msg":32,"data":33},"ok",{"site_id":25,"language":24,"slug":34,"title":13,"keywords":35,"description":14,"schema_data":36,"social_meta":88,"head_meta":90,"extra_data":92,"updated_unix":29},"quotient-complex-qc-based-machine-learning-for-2d-perovskite-design-a-preprint","",{"@graph":37,"@context":87},[38,55,70],{"@type":39,"itemListElement":40},"BreadcrumbList",[41,45,49,52],{"item":42,"name":43,"@type":44,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":46,"name":47,"@type":44,"position":48},"https://docshare.wps.com/document/","Document",2,{"item":50,"name":12,"@type":44,"position":51},"https://docshare.wps.com/document/research-report/",3,{"item":53,"name":13,"@type":44,"position":54},"https://docshare.wps.com/document/quotient-complex-qc-based-machine-learning-for-2d-perovskite-design-a-preprint/126171/",4,{"url":53,"name":13,"@type":56,"author":57,"headline":13,"publisher":59,"fileFormat":62,"inLanguage":24,"description":14,"dateModified":63,"datePublished":64,"encodingFormat":62,"isAccessibleForFree":65,"interactionStatistic":66},"DigitalDocument",{"name":9,"@type":58},"Person",{"url":42,"name":60,"@type":61},"DocShare","Organization","application/pdf","2026-08-25","2026-08-05",true,{"@type":67,"interactionType":68,"userInteractionCount":20},"InteractionCounter",{"@type":69},"ViewAction",{"@type":71,"mainEntity":72},"FAQPage",[73,79,83],{"name":74,"@type":75,"acceptedAnswer":76},"What problem does the paper address in designing 2D perovskites?","Question",{"text":77,"@type":78},"It addresses the limitation of inadequate material representations, which slows down the design and discovery of 2D perovskites.","Answer",{"name":80,"@type":75,"acceptedAnswer":81},"What is the quotient complex (QC) framework?",{"text":82,"@type":78},"The QC framework is a computational topology approach that provides a foundation for representing materials for downstream learning models.",{"name":84,"@type":75,"acceptedAnswer":85},"How do QC-based machine learning models perform compared with existing methods?",{"text":86,"@type":78},"Using the NMSE databank, the QC-based models show superior performance against all existing counterparts, emphasizing the importance of periodicity information.","https://schema.org",{"og:url":53,"og:type":89,"og:title":13,"og:site_name":60,"og:description":14},"article",{"robots":91,"canonical":53},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":94},[95,99,103,107,112,117,122,125,130,133,136],{"id":21,"doc_module":4,"doc_module_name":47,"category_name":96,"show_sort_weight":97,"slug":98},"Story & Novel",90,"story-novel",{"id":48,"doc_module":4,"doc_module_name":47,"category_name":100,"show_sort_weight":101,"slug":102},"Literature",80,"literature",{"id":54,"doc_module":4,"doc_module_name":47,"category_name":104,"show_sort_weight":105,"slug":106},"Exam",70,"exam",{"id":108,"doc_module":4,"doc_module_name":47,"category_name":109,"show_sort_weight":110,"slug":111},5,"Comic",60,"comic",{"id":113,"doc_module":4,"doc_module_name":47,"category_name":114,"show_sort_weight":115,"slug":116},6,"Technology",50,"technology",{"id":118,"doc_module":4,"doc_module_name":47,"category_name":119,"show_sort_weight":120,"slug":121},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":47,"category_name":12,"show_sort_weight":123,"slug":124},30,"research-report",{"id":126,"doc_module":4,"doc_module_name":47,"category_name":127,"show_sort_weight":128,"slug":129},9,"Religion & Spirituality",20,"religion-spirituality",{"id":128,"doc_module":4,"doc_module_name":47,"category_name":131,"show_sort_weight":128,"slug":132},"World Cup","world-cup",{"id":20,"doc_module":4,"doc_module_name":47,"category_name":134,"show_sort_weight":20,"slug":135},"Lifestyle","lifestyle",{"id":137,"doc_module":4,"doc_module_name":47,"category_name":138,"show_sort_weight":108,"slug":139},19,"General","general"]