[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-117948-en":3,"doc-seo-117948-105":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},117948,1649267921044,"Ava Thompson","https://us-avatar.wpscdn.com/avatar/1800007509477c92dfb?_k=1782875107921204101",8,"Research & Report","Mathematical optimization and machine learning to support PCB topology identification","This paper addresses an identification problem for schematics containing different concurring topologies. A hybrid framework is proposed that combines mathematical optimization with machine learning to determine and compare topology representations. The approach uses Python-based tooling, including scikit-rf for emulating network analyzer measurements and PCB microstrip line simulations, to generate training and testing data. An encoder-decoder model produces a flattened, topology-preserving graph representation, enabling latent-space optimization and reconstruction. Validation is demonstrated on a small circuit-topology model problem.","Adv. Radio Sci., 21, 25–35, 2023  \n[https://doi.org/10.5194/ars-21-25-2023](https://doi.org/10.5194/ars-21-25-2023)[ ](https://doi.org/10.5194/ars-21-25-2023)© Author(s) 2023 . This work is distributed under the Creative Commons Attribution 4 .0 License.  \nMathematical optimization and machine learning to support PCB topology identification  \nIlda Cahani and Marcus Stiemer  \nInstitute of the Theory of Electrical Engineering, Helmut Schmidt University, Hamburg, Germany Correspondence: Ilda Cahani ([ilda.cahani@hsu-hh.de](ilda.cahani@hsu-hh.de))  \nReceived: 7 February 2023 – Revised: 25 September 2023 – Accepted: 9 November 2023 – Published: 1 December 2023  \nAbstract. In this paper, we study an identification problem for schematics with different concurring topologies. A framework is proposed, that is both supported by mathematical optimization and machine learning algorithms. Through the use of Python libraries, such as scikit-rf, which allows for the emulation of network analyzer measurements, and a physical microstrip line simulation on PCBs, data for training and testing the framework are provided. In addition to an individual treatment of the concurring topologies and subsequent comparison, a method is introduced to tackle the identification of the optimum topology directly via a standard optimization or machine learning setup: An encoder-decoder sequence is trained with schematics of different topologies, to generate a flattened representation of the rated graph representation of the considered schematics. Still containing the relevant topology information in encoded (i.e., flattened) form, the so obtained latent space representations of schematics can be used for standard optimization of machine learning processes. Using now the encoder to map schematics on latent variables or the decoder to reconstruct schematics from their latent space representation, various machine learning and optimization setups can be applied to treat the given identification task. The proposed framework is presented and validated for a small model problem comprising different circuit topologies.  \n1 Introduction  \nPrinted circuit boards (PCB) are laminated sandwich structures of conductive and insulating layers connecting electronic components to one another that are used in almost every electronic product nowadays. The designing of PCBscan, however, be a very challenging task as it often takes a  \ngreat deal of knowledge and time to position hundreds of components and thousands of tracks into an intricate layout that meets a whole host of physical and electrical requirements (Jones, 2004) . As such, proper PCB design is an integral part of value added. There are three important factors tobe considered when designing a PCB: power integrity (PI), electromagnetic interference (EI), and signal integrity (SI), e.g., Archambeault and Drewniak (2013), of which will bethe focus of this paper.  \nThe availability of powerful simulation tools supporting the different phases of PCB design, i.e., generation of a schematics, placement of components (or modules), routing, and testing with respect to SI, PI, or EI, is essential for modern PCB design, e.g., Jansen et al. (2003), Wang et al. (2009) . However, in spite of the accessibility of such methods the extreme size of the configuration space makes PCB design still a hard and time-consuming task. For that reason, various approaches to the application of mathematical optimization and, particularly, machine learning to support electronics design have been recently undertaken, see, e.g., Li et al. (2021), Huang et al. (2021) .  \nOptimization and machine learning are both powerful problem-solving tools as long as the required type, quality, and quantity of data can be provided and sufficient – sometimes extensive – computing resources are available, particularly in case of real world problems. While an optimization method searches for good parameters in the design space by forecasting the shape of its target (or cost) f","cbCaickuLdwz2Cjf","https://ap.wps.com/l/cbCaickuLdwz2Cjf","pdf",2426901,1,11,"English","en",105,"# Introduction\n## PCB design challenges and motivation\n## Optimization and machine learning for electronics design\n## Data requirements and topology representation","[{\"question\":\"What problem does the paper focus on?\",\"answer\":\"It focuses on identifying schematics with different concurring topologies, treating the task as an identification problem supported by optimization and machine learning.\"},{\"question\":\"How is the proposed framework supported by tools and simulation data?\",\"answer\":\"Python libraries such as scikit-rf emulate network analyzer measurements, while physical microstrip line simulations on PCBs generate data for training and testing.\"},{\"question\":\"What role does the encoder-decoder model play?\",\"answer\":\"It trains on schematics of different topologies to generate a flattened, rated-graph-like representation in a latent space that still preserves topology information, enabling standard optimization or machine learning setups.\"}]","Mathematical optimization and machine learning to support PCB topology identification | 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problem does the paper focus on?","Question",{"text":76,"@type":77},"It focuses on identifying schematics with different concurring topologies, treating the task as an identification problem supported by optimization and machine learning.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"How is the proposed framework supported by tools and simulation data?",{"text":81,"@type":77},"Python libraries such as scikit-rf emulate network analyzer measurements, while physical microstrip line simulations on PCBs generate data for training and testing.",{"name":83,"@type":74,"acceptedAnswer":84},"What role does the encoder-decoder model play?",{"text":85,"@type":77},"It trains on schematics of different topologies to generate a flattened, rated-graph-like representation in a latent space that still preserves topology information, enabling standard optimization or machine learning 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