[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-123655-en":3,"doc-seo-123655-105":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},123655,549758146520,"Patrick","https://ap-avatar.wpscdn.com/avatar/80002397d8c0411e94?_k=1775819394049821470",8,"Research & Report","Beyond analytic approximations with machine learning inference of plasma parameters and confidence intervals - Paper","Machine learning techniques are used to build regression models that infer plasma state variables from both non-emissive (LP) and emissive (EP) cylindrical Langmuir probe measurements in regimes where standard analytic theories fail. Synthetic training and testing datasets are generated using plasma parameters and probe characteristics computed with the orbital motion theory framework. Model skill metrics quantify uncertainty margins for inferred parameters on unseen test sets, while scalings and transformations are optimized separately for LPs and EPs. Accurate inference is obtained for electron density, temperature, and plasma potential from LP characteristics, whereas EP results are dominated by strong plasma-potential dependence; only plasma-potential inferences are reported with acceptable accuracy. The work supports kinetic simulations plus machine learning as an efficient diagnostic route beyond analytic approximation validity.","J. Plasma Phys. (2023), vol. 89, 905890111 © The Author(s), 2023 . 1 Published by Cambridge University Press  \nThis is an Open Access article, distributed under the terms of the Creative Commons Attribution licence ([http://](http://)[ ](http://)[creativecommons.org/licenses/by/4.0](creativecommons.org/licenses/by/4.0)), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.  \ndoi:10.1017/S0022377823000041  \nBeyond analytic approximations with machine learning inference of plasma parameters and confidence intervals  \nRichard Marchand 1 ,†, Sadaf Shahsavani2 and Gonzalo Sanchez-Arriaga 2  \n1Department of Physics, University of Alberta, Edmonton, T6G 2E1, AB, Canada  \n2Aerospace Engineering Department, Universidad Carlos III de Madrid, Leganes, Madrid, Spain (Received 18 November 2022; revised 30 December 2022; accepted 4 January 2023)  \nMachine learning techniques are used to construct models capable of inferring plasma state variables from non-emissive (LP) and emissive (EP) cylindrical Langmuir probes under conditions in which standard analytic theories are not applicable. Synthetic datasets, consisting of plasma parameters and probe characteristics computed kinetically in the orbital motion theory framework, are used to train and test regression models to infer electron densities, temperatures, and plasma potentials. Model skill metrics are introduced to determine uncertainty margins on inferred parameters, when models are applied to test sets not involved in the model optimization process. The different scalings and transformations required to obtain optimal accuracy are described in each case considered for both LPs and EPs. Excellent inferences are made for all three parameters considered from LP characteristics, but owing to the strong dependence on the plasma potential, and weak dependences on electron temperature and density with EPs, only plasma potential inferences are reported with acceptable accuracy for this type of probe. Our findings demonstrate that the combination of kinetic simulations and machine learning techniques is a promising and practical way to infer plasma parameters efficiently from cylindrical probes, under conditions beyond, and more general than those under which commonly used analytic approximations are valid.  \nKey words: plasma inferences, orbital-motion-theory, multivariate regressions  \n1. Introduction  \nThe inference of plasma parameters, like plasma density and temperature from Langmuir and emissive probe measurements, is generally made with theoretical models. Orbital motion theory (OMT) (Laframboise 1966) for cylindrical probes immersed at rest in a collisionless and unmagnetized plasma and without particle trapping is one of several such models. However, the OMT is based on the solutions of the Vlasov–Poisson system, and it does not provide, in general, analytical relations between the collected current and the plasma parameters to be used easily in the interpretation of experimental  \n†Email address for correspondence: [rmarchan@ualberta.ca](rmarchan@ualberta.ca)  \n[https://doi.org/10.1017/S0022377823000041](https://doi.org/10.1017/S0022377823000041) Published online by Cambridge University Press  \n2 R. Marchand, S. Shahsavani and G. Sanchez-Arriaga  \ncurrent–voltage (I–V) characteristics from both emissive and non-emissive cylindrical probes. Only within a subset of the physical parameters that make the probe operate in the so-called orbital-motion-limited regime (OML), like for instance for a small enough probe radius-to-Debye length ratio (Sanmartín & Estes 1999), does the OMT provide simple and analytical results for the collected currents. Beyond such a particular regime, the most the OMT can provide is a large database of current–voltage characteristics for Langmuir (Laframboise 1966) and emissive (Shahsavani, Chen & Sanchez-Arriaga 2021b) probes based on numerical solutions of the Vlasov–Poisson system.  \nTo ease their use","cbCaimdxHt6kXzHf","https://ap.wps.com/l/cbCaimdxHt6kXzHf","pdf",1091704,1,12,"English","en",105,"# Introduction\n## Plasma parameter inference from Langmuir probe measurements\n## Orbital motion theory and its limitations\n## Analytical fitting laws and regression approaches\n# Methodology\n## Multivariate regression based on OMT solution libraries","[{\"question\":\"Why do the results differ between non-emissive and emissive cylindrical probes?\",\"answer\":\"For LPs, all three parameters can be inferred accurately from probe characteristics. For EPs, plasma potential strongly controls the measurements, while electron temperature and density dependencies are weak, so only plasma-potential inference is reported with acceptable accuracy.\"}]","Beyond analytic approximations with machine learning inference of plasma parameters and confidence intervals - Paper | PDF",1785817858,30,{"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},"beyond-analytic-approximations-with-machine-learning-inference-of-plasma-parameters-and-confidence-intervals-paper","",{"@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/beyond-analytic-approximations-with-machine-learning-inference-of-plasma-parameters-and-confidence-intervals-paper/123655/",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","2026-08-04",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71],{"name":72,"@type":73,"acceptedAnswer":74},"Why do the results differ between non-emissive and emissive cylindrical probes?","Question",{"text":75,"@type":76},"For LPs, all three parameters can be inferred accurately from probe characteristics. 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