{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/model-agnostic-basis-functions-for-the-2","title":"Model-agnostic basis functions for the 2-point correlation function of dark matter in linear theory","arxiv_id":"2410.21374","date":"2024-10-28","proceeding":null,"authors":["Aseem Paranjape","Ravi K. Sheth"],"abstract":"We consider approximating the linearly evolved 2-point correlation function (2pcf) of dark matter $\\xi_{\\rm lin}(r;\\boldsymbol{\\theta})$ in a cosmological model with parameters $\\boldsymbol{\\theta}$ as the linear combination $\\xi_{\\rm lin}(r;\\boldsymbol{\\theta})\\approx\\sum_i\\,b_i(r)\\,w_i(\\boldsymbol{\\theta})$, where the functions $\\mathcal{B}=\\{b_i(r)\\}$ form a $\\textit{model-agnostic basis}$ for the linear 2pcf. This decomposition is important for model-agnostic analyses of the baryon acoustic oscillation (BAO) feature in the nonlinear 2pcf of galaxies that fix $\\mathcal{B}$ and leave the coefficients $\\{w_i\\}$ free. To date, such analyses have made simple but sub-optimal choices for $\\mathcal{B}$, such as monomials. We develop a machine learning framework for systematically discovering a $\\textit{minimal}$ basis $\\mathcal{B}$ that describes $\\xi_{\\rm lin}(r)$ near the BAO feature in a wide class of cosmological models. We use a custom architecture, denoted $\\texttt{BiSequential}$, for a neural network (NN) that explicitly realizes the separation between $r$ and $\\boldsymbol{\\theta}$ above. The optimal NN trained on data in which only $\\{\\Omega_{\\rm m},h\\}$ are varied in a $\\textit{flat}$ $\\Lambda$CDM model produces a basis $\\mathcal{B}$ comprising $9$ functions capable of describing $\\xi_{\\rm lin}(r)$ to $\\sim0.6\\%$ accuracy in $\\textit{curved}$ $w$CDM models varying 7 parameters within $\\sim5\\%$ of their fiducial, flat $\\Lambda$CDM values. Scales such as the peak, linear point and zero-crossing of $\\xi_{\\rm lin}(r)$ are also recovered with very high accuracy. We compare our approach to other compression schemes in the literature, and speculate that $\\mathcal{B}$ may also encompass $\\xi_{\\rm lin}(r)$ in modified gravity models near our fiducial $\\Lambda$CDM model. Using our basis functions in model-agnostic BAO analyses can potentially lead to significant statistical gains.","url_abs":"https://arxiv.org/abs/2410.21374v2","url_pdf":"https://arxiv.org/pdf/2410.21374v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"model-agnostic-basis-functions-for-the-2","repo_url":"https://github.com/a-paranjape/mlfundas","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[],"methods":[{"method_slug":"gravity","method_name":"Gravity"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}