Cosmology-informed neural networks to solve the background dynamics of the Universe

Abstract

The field of machine learning has drawn increasing interest from various other fields due to the success of its methods at solving a plethora of different problems. An application of these has been to train artificial neural networks to solve differential equations without the need of a numerical solver. This particular application offers an alternative to conventional numerical methods, with advantages such as lower memory required to store solutions, parallelization, and, in some cases, a lower overall computational cost than its numerical counterparts. In this work, we train artificial neural networks to represent a bundle of solutions of the differential equations that govern the background dynamics of the Universe for four different models. The models we have chosen are $\Lambda \mathrm{CDM}$, the Chevallier-Polarski-Linder parametric dark energy model, a quintessence model with an exponential potential, and the Hu-Sawicki $f(R)$ model. We use the solutions that the networks provide to perform statistical analyses to estimate the values of each model's parameters with observational data; namely, estimates of the Hubble parameter from cosmic chronometers, type Ia supernovae data from the Pantheon compilation, and measurements from baryon acoustic oscillations. The results we obtain for all models match similar estimations done in the literature using numerical solvers. In addition, we estimate the error of the solutions that the trained networks provide by comparing them with the analytical solution when there is one, or to a high-precision numerical solution when there is not. Through these estimations we find that the error of the solutions is at most $\sim 1\%$ in the region of the parameter space that concerns the $95\%$ confidence regions that we find using the data, for all models and all statistical analyses performed in this work.

28 pages, 10 figures, 10 tables, supplemental material available at https://github.com/at-chantada/Supplemental-Materials

References in corpus (15)

• Cosmology and the Fate of Dilatation Symmetry
• A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km/s/Mpc Uncertainty from the Hubble Space Telescope and the SH0ES Team
• The Clustering of the SDSS DR7 Main Galaxy Sample I: A 4 per cent Distance Measure at z=0.15
• Models of f(R) Cosmic Acceleration that Evade Solar-System Tests
• Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z$\sim$2
• The Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: measurement of the BAO and growth rate of structure of the luminous red galaxy sample from the anisotropic correlation function between redshifts 0.6 and 1
• f(R) Gravity and Chameleon Theories
• Baryon acoustic oscillations from the complete SDSS-III Ly$\alpha$-quasar cross-correlation function at $z=2.4$
• Equivalence Principle Implications of Modified Gravity Models
• A buyer's guide to the Hubble Constant
• COSMOPOWER: emulating cosmological power spectra for accelerated Bayesian inference from next-generation surveys
• Solving differential equations with neural networks: Applications to the calculation of cosmological phase transitions
• Neural Network Reconstruction of Late-Time Cosmology and Null Tests
• Testing f(R) gravity models with quasar X-ray and UV fluxes
• Spatial Curvature in $f(R)$ Gravity

Cited by in corpus (11)

• Non-parametric reconstruction of cosmological observables using Gaussian Processes Regression
• Testing f(R)-gravity models with DESI DR2 2025-BAO and other cosmological data
• Solving the Pulsar Equation using Physics-Informed Neural Networks
• Probing the H0 Tension with Holographic Dark Energy in Unimodular Gravity: Insights from DESI DR2
• Inferring Cosmological Parameters with Evidential Physics-Informed Neural Networks
• Faster Bayesian inference with neural network bundles and new results for $f(R)$ models
• Hubble Tension and Dark Energy in Teleparallel Gauss-Bonnet Gravity: New Constraints from DESI BAO, Pantheon${}^{+}$ and Hubble Data
• Unraveling particle dark matter with Physics-Informed Neural Networks
• Acceleration Potential and Density Profile of Secondary Plasma in the Magnetosphere of Orthogonal Pulsars
• Observational constraints on Luciano-Saridakis entropic cosmology
• Evolution of linear matter perturbations with error-bounded bundle physics-informed neural networks