Interpretable and physics-informed emulator for the linear matter power spectrum from machine learning
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| Format: | Preprint |
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2024
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| author | Orjuela-Quintana, J. Bayron Sapone, Domenico Nesseris, Savvas |
| author_facet | Orjuela-Quintana, J. Bayron Sapone, Domenico Nesseris, Savvas |
| contents | We present an interpretable emulator for the linear matter power spectrum (MPS) in the standard cosmological model $Λ$CDM, constructed via a physics-informed symbolic regression framework. By combining domain knowledge with a machine learning technique known as genetic algorithms, we explore the space of analytic expressions to derive closed-form, smooth, physically motivated approximations of the MPS that match the accuracy of standard broadband reconstruction methodologies such as the Savitzky-Golay filter. Building upon this baseline, we incorporate transparent oscillatory corrections informed by the physics of baryon acoustic oscillations (BAO). The resulting expression delivers mean sub-percent fractional errors across a broad range of scales ($k \in [10^{-5}, 1.5]~h\,\mathrm{Mpc}^{-1}$) with an average deviation of $\sim 0.4\%$ when tested against spectra computed with a Boltzmann solver. Moreover, a comparable level of fractional deviation is maintained on smaller scales when the GA-derived formulation is used as input to the nonlinear emulator halofit. To illustrate the versatility of the framework beyond $Λ$CDM, we apply it to a representative $f(R)$ gravity model. Rather than training a general modified-gravity emulator, we compute the corresponding linear spectra with a Boltzmann solver and fit a parametric deformation of the $Λ$CDM smoothed component. This procedure achieves average errors at the 1.5-1.8\% level and captures the leading modulation of the MPS induced by modified gravity, enabling a controlled study of its impact on the BAO scale. Our results provide compact, accurate, and physically motivated fitting functions for the linear MPS in both standard and MG cosmologies, offering a fast and transparent alternative to existing emulators for parameter inference and theoretical modeling in large-scale structure analyses. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_16640 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Interpretable and physics-informed emulator for the linear matter power spectrum from machine learning Orjuela-Quintana, J. Bayron Sapone, Domenico Nesseris, Savvas Cosmology and Nongalactic Astrophysics We present an interpretable emulator for the linear matter power spectrum (MPS) in the standard cosmological model $Λ$CDM, constructed via a physics-informed symbolic regression framework. By combining domain knowledge with a machine learning technique known as genetic algorithms, we explore the space of analytic expressions to derive closed-form, smooth, physically motivated approximations of the MPS that match the accuracy of standard broadband reconstruction methodologies such as the Savitzky-Golay filter. Building upon this baseline, we incorporate transparent oscillatory corrections informed by the physics of baryon acoustic oscillations (BAO). The resulting expression delivers mean sub-percent fractional errors across a broad range of scales ($k \in [10^{-5}, 1.5]~h\,\mathrm{Mpc}^{-1}$) with an average deviation of $\sim 0.4\%$ when tested against spectra computed with a Boltzmann solver. Moreover, a comparable level of fractional deviation is maintained on smaller scales when the GA-derived formulation is used as input to the nonlinear emulator halofit. To illustrate the versatility of the framework beyond $Λ$CDM, we apply it to a representative $f(R)$ gravity model. Rather than training a general modified-gravity emulator, we compute the corresponding linear spectra with a Boltzmann solver and fit a parametric deformation of the $Λ$CDM smoothed component. This procedure achieves average errors at the 1.5-1.8\% level and captures the leading modulation of the MPS induced by modified gravity, enabling a controlled study of its impact on the BAO scale. Our results provide compact, accurate, and physically motivated fitting functions for the linear MPS in both standard and MG cosmologies, offering a fast and transparent alternative to existing emulators for parameter inference and theoretical modeling in large-scale structure analyses. |
| title | Interpretable and physics-informed emulator for the linear matter power spectrum from machine learning |
| topic | Cosmology and Nongalactic Astrophysics |
| url | https://arxiv.org/abs/2407.16640 |