[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-119914-en":3,"doc-seo-119914-105":30,"detail-sidebar-cat-0-en-105":95},{"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},119914,3848291630094,"Emma Wilson","https://eur-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45",8,"Research & Report","Machine learning and structure formation in modified gravity","In general relativity, approximations built on the spherical collapse model—such as Press–Schechter theory and its extensions—aim to predict the abundance of objects across mass scales in a given volume. This work applies a machine-learning approach to test whether these approximations remain valid in screened modified-gravity theories. Random-forest models are trained on N-body simulation data for both ΛCDM and screened modified gravity, specifically f(R) and nDGP. The method learns to identify structure membership in final states from initial-condition density-field behavior, and evaluates how well a ΛCDM-trained model generalizes across modified-gravity strengths.","This is a repository copy of Machine learning and structure formation in modified gravity.  \nWhite Rose Research Online URL for this paper:  \n[https://eprints.whiterose.ac.uk/210739/](https://eprints.whiterose.ac.uk/210739/)  \nVersion: Published Version  \nArticle:  \nBetts, J.C., van de Bruck, C., Arnold, [C. orcid.org/0000-0002-7304-0519](C. orcid.org/0000-0002-7304-0519) et al. (1 more author) (2023) Machine learning and structure formation in modified gravity. Monthly Notices of the Royal Astronomical Society, 526 (3) . pp. 4148-4156. ISSN 0035-8711  \n[https://doi.org/10.1093/mnras/stad2915](https://doi.org/10.1093/mnras/stad2915)  \nThis article has been accepted for publication in Monthly Notices of the Royal Astronomical Society © 2023 The Author(s) . Published by Oxford University Press on behalf of the Royal Astronomical Society. All rights reserved.  \nReuse  \nItems deposited in White Rose Research Online are protected by copyright, with all rights reserved unless indicated otherwise. They may be downloaded and/or printed for private study, or other acts as permitted by national copyright laws. The publisher or other rights holders may allow further reproduction and re-use of the full text version. This is indicated by the licence information on the White Rose Research Online record for the item.  \nTakedown  \nIf you consider content in White Rose Research Online to be in breach of UK law, please notify us by  \nemailing [eprints@whiterose.ac.uk](eprints@whiterose.ac.uk) including the URL of the record and the reason for the withdrawal request.  \n[eprints@whiterose.ac.uk](eprints@whiterose.ac.uk)[ ](eprints@whiterose.ac.uk)[https://eprints.whiterose.ac.uk/](https://eprints.whiterose.ac.uk/)  \nMNRAS 526, 4148–4156 (2023) [https://doi.org/10.1093/mnras/stad2915](https://doi.org/10.1093/mnras/stad2915)  \nAdvance Access publication 2023 September 29  \nMachine learning and structure formation in modified gravity  \nJonathan C. Betts, 1‹ Carsten van de Bruck,1 Christian Arnold 2 and Baojiu Li 2  \n1School of Mathematics and Statistics, University of Sheffield, Hounsfield Road, S3 7RH Sheffield, United Kingdom  \n2Institute for Computational Cosmology, Department of Physics, Durham University, South Road, Durham DH1 3LE, United Kingdom  \nAccepted 2023 September 20. Received 2023 August 26; in original form 2023 May 26  \nABSTRACT  \nIn general relativity, approximations based on the spherical collapse model such as Press–Schechter theory and its extensions are able to predict the number of objects of a certain mass in a given volume. In this paper, we use a machine learning algorithm to test whether such approximations hold in screened modi􀀞ed gravity theories. To this end, we train random forest classi􀀞erson data from N-body simulations to study the formation of structures in lambda cold dark matter (􀀂CDM) as well as screened modi􀀞ed gravity theories, in particular f(R) and nDGP gravity. The models are taught to distinguish structure membership in the 􀀞nal conditions from spherical aggregations of density 􀀞eld behaviour in the initial conditions. We examine the differences between machine learning models that have learned structure formation from each gravity, as well as the model that has learned from 􀀂CDM. We also test the generalizability of the 􀀂CDM model on data from f(R) and nDGP gravities of varying strengths, and therefore the generalizability of extended Press–Schechter spherical collapse to these types of modi􀀞ed gravity.  \nKey words: dark energy–dark matter–large-scale structure of Universe.  \n1 INTRODUCTION  \nStructure formation in the Universe is caused by gravitational instability due to tiny density uctuations produced in the very early Universe. It proceeds from the bottom up, with objects smaller than galaxies forming 􀀞rst, which subsequently form larger structures such as galaxies and clusters of galaxies. An important ingredient in this theory is the existence of dark matter (DM), which allows structures to form on sma","cbCaitU6qLPwyZXL","https://ap.wps.com/l/cbCaitU6qLPwyZXL","pdf",957017,1,10,"English","en",105,"# Abstract\n# 1 Introduction\n## Structure formation and gravitational instability\n## Dark matter haloes and non-linear evolution\n## (Semi-)analytic approximations and Press–Schechter framework\n## Motivation from cosmic acceleration and modified gravity models","[{\"question\":\"What is the main goal of applying machine learning in this paper?\",\"answer\":\"To test whether spherical-collapse-based approximations such as Press–Schechter remain valid in screened modified-gravity theories.\"},{\"question\":\"Which gravity models and data sources are used for training?\",\"answer\":\"Random-forest classifiers are trained using N-body simulation data for ΛCDM as well as screened modified gravity, particularly f(R) and nDGP.\"},{\"question\":\"How do the machine-learning models interpret the initial conditions?\",\"answer\":\"They learn to distinguish structure membership in final conditions based on density-field behavior in the initial conditions.\"},{\"question\":\"Does the paper evaluate whether a model trained on ΛCDM works for modified gravity?\",\"answer\":\"Yes. It tests generalizability by applying a ΛCDM-trained model to f(R) and nDGP data with varying strengths, assessing the broader validity of extended Press–Schechter spherical collapse.\"}]","Machine learning and structure formation in modified gravity | PDF",1785726981,25,{"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":90,"head_meta":92,"extra_data":94,"updated_unix":28},"machine-learning-and-structure-formation-in-modified-gravity","",{"@graph":36,"@context":89},[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/machine-learning-and-structure-formation-in-modified-gravity/119914/",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","2026-08-03",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81,85],{"name":72,"@type":73,"acceptedAnswer":74},"What is the main goal of applying machine learning in this paper?","Question",{"text":75,"@type":76},"To test whether spherical-collapse-based approximations such as Press–Schechter remain valid in screened modified-gravity theories.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"Which gravity models and data sources are used for training?",{"text":80,"@type":76},"Random-forest classifiers are trained using N-body simulation data for ΛCDM as well as screened modified gravity, particularly f(R) and nDGP.",{"name":82,"@type":73,"acceptedAnswer":83},"How do the machine-learning models interpret the initial conditions?",{"text":84,"@type":76},"They learn to distinguish structure membership in final conditions based on density-field behavior in the initial conditions.",{"name":86,"@type":73,"acceptedAnswer":87},"Does the paper evaluate whether a model trained on ΛCDM works for modified gravity?",{"text":88,"@type":76},"Yes. It tests generalizability by applying a ΛCDM-trained model to f(R) and nDGP data with varying strengths, assessing the broader validity of extended Press–Schechter spherical collapse.","https://schema.org",{"og:url":52,"og:type":91,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":93,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":96},[97,101,105,109,114,119,124,127,132,135,138],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":106,"show_sort_weight":107,"slug":108},"Exam",70,"exam",{"id":110,"doc_module":4,"doc_module_name":46,"category_name":111,"show_sort_weight":112,"slug":113},5,"Comic",60,"comic",{"id":115,"doc_module":4,"doc_module_name":46,"category_name":116,"show_sort_weight":117,"slug":118},6,"Technology",50,"technology",{"id":120,"doc_module":4,"doc_module_name":46,"category_name":121,"show_sort_weight":122,"slug":123},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":125,"slug":126},30,"research-report",{"id":128,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":130,"slug":131},9,"Religion & Spirituality",20,"religion-spirituality",{"id":130,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":130,"slug":134},"World Cup","world-cup",{"id":21,"doc_module":4,"doc_module_name":46,"category_name":136,"show_sort_weight":21,"slug":137},"Lifestyle","lifestyle",{"id":139,"doc_module":4,"doc_module_name":46,"category_name":140,"show_sort_weight":110,"slug":141},19,"General","general"]