{"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/a-multi-fidelity-emulator-for-the-matter","title":"Multi-Fidelity Emulation for the Matter Power Spectrum using Gaussian Processes","arxiv_id":"2105.01081","date":"2021-05-03","proceeding":null,"authors":["Ming-Feng Ho","Simeon Bird","Christian R. Shelton"],"abstract":"We present methods for emulating the matter power spectrum by combining information from cosmological $N$-body simulations at different resolutions. An emulator allows estimation of simulation output by interpolating across the parameter space of a limited number of simulations. We present the first implementation in cosmology of multi-fidelity emulation, where many low-resolution simulations are combined with a few high-resolution simulations to achieve an increased emulation accuracy. The power spectrum's dependence on cosmology is learned from the low-resolution simulations, which are in turn calibrated using high-resolution simulations. We show that our multi-fidelity emulator predicts high-fidelity counterparts to percent-level relative accuracy when using only $3$ high-fidelity simulations and outperforms a single-fidelity emulator that uses $11$ simulations, although we do not attempt to produce a converged emulator with high absolute accuracy. With a fixed number of high-fidelity training simulations, we show that our multi-fidelity emulator is $\\simeq 100$ times better than a single-fidelity emulator at $k \\leq 2 h \\mathrm{Mpc}^{-1}$, and $\\simeq 20$ times better at $3 \\leq k < 6.4 h \\mathrm{Mpc}^{-1}$. Multi-fidelity emulation is fast to train, using only a simple modification to standard Gaussian processes. Our proposed emulator shows a new way to predict non-linear scales by fusing simulations from different fidelities.","url_abs":"https://arxiv.org/abs/2105.01081v2","url_pdf":"https://arxiv.org/pdf/2105.01081v2.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":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"a-multi-fidelity-emulator-for-the-matter","repo_url":"https://github.com/jibanCat/matter_multi_fidelity_emu","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}