[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-122642-en":3,"doc-seo-122642-105":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},122642,687197100911,"Himbo","https://ap-avatar.wpscdn.com/avatar/a000239b6f1da00475?x-image-process=image/resize,m_fixed,w_180,h_180&k=1785132997149421697",8,"Research & Report","Tackling multimodal device distributions in inverse photonic design using invertible neural networks","We show how conditional generative neural networks efficiently identify nanophotonic devices with target properties, enabling inverse photonic design. Machine learning helps overcome challenges from the dimensionality and topology of design parameter spaces. Traditional inverse methods often rely on an invertible parameter-to-response mapping, but distinct designs can achieve equal or comparable performance, creating multimodal solution sets that hinder convergence. We use generative modeling to output the full distribution of feasible solutions, including multiple modes. We compare a conditional variational autoencoder (cVAE) with a conditional invertible neural network (cINN) on a nanophotonic transmission-spectrum design task. Results demonstrate that cINNs offer greater flexibility for multimodal device distributions.","Mach. Learn.: Sci. Technol. 4 (2023) 02LT02 [https://doi.org/10.1088/2632-2153/acd619](https://doi.org/10.1088/2632-2153/acd619)  \nOPEN ACCESS  \nRECEIVED  \n21 March 2023  \nREVISED  \n19 April 2023  \nACCEPTED FOR PUBLICATION 16 May 2023  \nPUBLISHED  \n31 May 2023  \nOriginal content from this work may be used under the terms of the  \nCreative Commons Attribution 4 .0 licence.  \nAny further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.  \nLETTER  \nTackling multimodal device distributions in inverse photonic design using invertible neural networks  \nMichel Frising1, ∗􀁂, Jorge Bravo-Abad2􀁂 and Ferry Prins1􀁂  \n1 Condensed Matter Physics Center (IFIMAC) and Department of Condensed Matter Physics, Autonomous University of Madrid, 28049 Madrid, Spain  \n2 Condensed Matter Physics Center (IFIMAC) and Department of Theoretical Condensed Matter Physics, Autonomous University of Madrid, 28049 Madrid, Spain  \n∗ Author to whom any correspondence should be addressed.  \n[E-mail: michel.frising@uam.es](E-mail: michel.frising@uam.es)  \nKeywords: nanotechnology, inverse design, multimodality, machine learning, invertible neural networks, nanophotonics, generative modeling  \nSupplementary material for this article is available online  \nAbstract  \nWe show how conditional generative neural networks can be used to efficiently find nanophotonic devices with desired properties, also known as inverse photonic design. Machine learning has emerged as a promising approach to overcome limitations imposed by the dimensionality and topology of the parameter space. Importantly, traditional optimization routines assume an invertible mapping between the design parameters and response. However, different designs may have comparable or even identical performance confusing the optimization algorithm when performing inverse design. Our generative modeling approach provides the full distribution of possible solutions to the inverse design problem, including multiple solutions. We compare a commonly used conditional variational autoencoder (cVAE) and a conditional invertible neural network (cINN) on a proof-of-principle nanophotonic problem, consisting in tailoring the transmission spectrum trough a metallic film milled by subwavelength indentations. We show how cINNs have superior flexibility compared to cVAEs when dealing with multimodal device distributions.  \n1. Introduction  \nInverse design is the process of matching a device or process parameters to produce a desired performance. The possibility of enabling new materials and nanodevices by ‘reverse-engineering’ them from the desired properties and characteristics has drawn a great deal of both fundamental and applied interest. Inverse design is particularly popular in the field of nanophotonics, where the ongoing quest for miniaturization requires the exploration of extremely large parameter spaces spanned by freeform geometries and a wide variety of materials combinations. To efficiently explore these vast parameter spaces, the inverse-design problem is commonly approached using computational optimization techniques capable of identifying solutions beyond human intuition. Techniques such as gradient-based topology optimization [1–5], evolutionary design [6, 7] and more recently artificial neural networks [8–11] and global optimization nets [12, 13] have been used successfully to design devices that vastly outperform designs based on human intuition.  \nTo date, however, most inverse design approaches rely on the assumption that a unique one-to-one mapping exists between the device and a given design target. In reality, it is often the case that multiple device designs exhibit comparable or even identical performance, yielding a multimodal device distribution. One clear example of this phenomenon are systems or devices with symmetries. For example, the structure shown in figure 1 (which we will use throughout this manuscript for illustrative ","cbCaialhQQLWIoJQ","https://ap.wps.com/l/cbCaialhQQLWIoJQ","pdf",1008516,1,"English","en",105,"# Introduction\n## Inverse design and computational optimization\n## Multimodality challenge and symmetry example","[{\"question\":\"What is inverse photonic design in this work?\",\"answer\":\"It is the task of matching device or process parameters to achieve a desired photonic performance, such as a targeted transmission spectrum.\"},{\"question\":\"Why does multimodality make inverse design difficult for standard optimization?\",\"answer\":\"Different device geometries can produce comparable or identical performance, so the assumed one-to-one mapping breaks down and optimization may oscillate instead of converging.\"},{\"question\":\"How do conditional invertible neural networks help compared with conditional variational autoencoders?\",\"answer\":\"They provide more flexibility for multimodal solution distributions and better capture multiple feasible designs instead of collapsing to a single solution.\"}]","Tackling multimodal device distributions in inverse photonic design using invertible neural networks | 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is inverse photonic design in this work?","Question",{"text":74,"@type":75},"It is the task of matching device or process parameters to achieve a desired photonic performance, such as a targeted transmission spectrum.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"Why does multimodality make inverse design difficult for standard optimization?",{"text":79,"@type":75},"Different device geometries can produce comparable or identical performance, so the assumed one-to-one mapping breaks down and optimization may oscillate instead of converging.",{"name":81,"@type":72,"acceptedAnswer":82},"How do conditional invertible neural networks help compared with conditional variational autoencoders?",{"text":83,"@type":75},"They provide more flexibility for multimodal solution distributions and better capture multiple feasible designs instead of collapsing to a single 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