[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-125749-en":3,"doc-seo-125749-105":30,"detail-sidebar-cat-0-en-105":91},{"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},125749,3848291630094,"Emma Wilson","https://eur-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45",8,"Research & Report","Galaxy Rotation Curve Fitting Using Machine Learning Tools","Galaxy rotation curve (RC) fitting constrains dark matter (DM) halo models by matching observed rotational velocities as a function of galactocentric radius. For non-phenomenological DM profiles lacking analytic expressions, optimizing full baryonic plus DM parameters is often time-consuming. This work applies a gradient-descent method from neural-network training to fit the Milky Way’s Grand Rotation Curve from about 1 pc to 10^5 pc, using a semi-analytical bulge+disk+fermionic RAR halo model. Results provide best-fit parameters across 10^2–10^5 pc in only a few hours of CPU time.","universe   \nArticle  \nGalaxy Rotation Curve Fitting Using Machine Learning Tools  \nCarlos R. Argüelles 1,2, *,† and Santiago Collazo 1, *,†  \nCitation: Argüelles, C.R.; Collazo S. Galaxy Rotation Curve Fitting Using Machine Learning Tools. Universe 2023, 9, 372. [https://doi.org/](https://doi.org/)[ ](https://doi.org/)[10.3390/universe9080372](10.3390/universe9080372)  \nAcademic Editors: Stephen J. Curran and Nicola R. Napolitano  \nReceived: 5 July 2023  \nRevised: 10 August 2023  \nAccepted: 14 August 2023  \nPublished: 16 August 2023  \nCopyright: © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license ([https://](https://)[ ](https://)[creativecommons.org/licenses/by/](creativecommons.org/licenses/by/)[ ](creativecommons.org/licenses/by/)[4.0/](4.0/)) .  \n1 Instituto de Astrofísica de La Plata, UNLP-CONICET, Paseo del Bosque s/n, La Plata B1900FWA, Argentina  \n2 ICRANet, Piazza della Repubblica 10, I-65122 Pescara, Italy  \n* Correspondence: [carguelles@fcaglp.unlp.edu.ar](carguelles@fcaglp.unlp.edu.ar) (C.R.A.); [scollazo@fcaglp.unlp.edu.ar](scollazo@fcaglp.unlp.edu.ar) (S.C.)† These authors contributed equally to this work.  \nAbstract: Galaxy rotation curve (RC) ﬁtting is an important technique which allows the placement of constraints on different kinds of dark matter (DM) halo models. In the case of non-phenomenological DM proﬁles with no analytic expressions, the art of ﬁnding RC best-ﬁts including the full baryonic + DM free parameters can be difﬁcult and time-consuming. In the present work, we use a gradient descent method used in the backpropagation process of training a neural network, to ﬁt the socalled Grand Rotation Curve of the Milky Way (MW) ranging from 􀀘 1 pc all the way to 􀀘 105 pc. We model the mass distribution of our Galaxy including a bulge (inner + main), a disk, anda fermionic dark matter (DM) halo known as the Rufﬁni-Argüelles-Rueda (RAR) model. This is a semi-analytical model built from ﬁrst-principle physics such as (quantum) statistical mechanics and thermodynamics, whose more general density proﬁle has a dense core–diluted halo morphology with no analytic expression. As shown recently and further veriﬁed here, the dark and compact fermion-core can work as an alternative to the central black hole in SgrA* when including data at milliparsec scales from the S-cluster stars. Thus, we show the ability of this state-of-the-art machine learning tool in providing the best-ﬁt parameters to the overall MW RC in the 10􀀀2–105 pc range, in a few hours of CPU time.  \nKeywords: dark matter; Milky Way; rotation curves; numerical methods  \n1. Introduction  \nDisk galaxies, like our own, are rotational supported structures with the advantage of having baryonic (or luminous) mass tracers in approximate circular orbits from which it is possible to obtain the so-called RC. The speciﬁc DM distribution, usually dubbed asthe DM density proﬁle, is inferred by ﬁtting the observed velocity RC as a function of the galactocentric radius. Typically, this is carried out by assuming a given underlying DM proﬁle together with different mass models for the luminous components such as the bulge, disc, etc. (see, e.g., [1] for a review) . Most of these studies assume phenomenological DM proﬁles (in spherical symmetry) obtained from classical N-body cosmological simulations with a given analytic expression, besides the visible mass components. However, other kinds of DM proﬁles can be obtained from ﬁrst-principle physics (i.e., thermodynamics and statistical mechanics) while accounting for the quantum nature of the particles, such asthe RAR model for fermions (see [2] for a review, and references therein) and, e.g., [3,4] for bosonic DM, with no analytic expressions for the proﬁles.  \nThe RAR model consist in a self-gravitating system of fermions in General Relativity, and therefore is built upon a couple","cbCaiqGgL56ISjqH","https://ap.wps.com/l/cbCaiqGgL56ISjqH","pdf",1237361,1,9,"English","en",105,"# Introduction\n## Dark matter density profiles and rotation curve fitting\n## First-principle DM models and the RAR fermion halo\n# Method background\n## RAR model equations and free parameters\n## Boundary conditions from observations and core–halo solutions\n# Machine-learning fitting approach\n## Gradient descent and training-inspired optimization\n# Results and implications\n## Best-fit Milky Way rotation-curve parameters and computational performance","[{\"question\":\"Why is galaxy rotation curve fitting important for dark matter studies?\",\"answer\":\"It links observed rotational velocities to the inferred DM density profile by fitting velocity as a function of radius, providing constraints on halo models.\"},{\"question\":\"What problem does this paper address with non-phenomenological DM profiles?\",\"answer\":\"Such profiles often lack analytic expressions, making the search for best-fit parameters—including full baryonic and DM degrees of freedom—difficult and time-consuming.\"},{\"question\":\"How does the proposed machine learning method perform the fitting?\",\"answer\":\"It uses a gradient descent strategy inspired by neural-network backpropagation to optimize model parameters and fit the Milky Way’s rotation curve over parsec to kiloparsec scales.\"}]","Galaxy Rotation Curve Fitting Using Machine Learning Tools | 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is galaxy rotation curve fitting important for dark matter studies?","Question",{"text":75,"@type":76},"It links observed rotational velocities to the inferred DM density profile by fitting velocity as a function of radius, providing constraints on halo models.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What problem does this paper address with non-phenomenological DM profiles?",{"text":80,"@type":76},"Such profiles often lack analytic expressions, making the search for best-fit parameters—including full baryonic and DM degrees of freedom—difficult and time-consuming.",{"name":82,"@type":73,"acceptedAnswer":83},"How does the proposed machine learning method perform the fitting?",{"text":84,"@type":76},"It uses a gradient descent strategy inspired by neural-network backpropagation to optimize model parameters and fit the Milky Way’s rotation curve over parsec to kiloparsec 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