Evolution of linear matter perturbations with error-bounded bundle physics-informed neural networks

TL;DR

This paper introduces an error-bounded physics-informed neural network approach to model the evolution of linear matter perturbations in cosmology, providing more accurate predictions and tighter constraints on key parameters.

Contribution

It develops a novel PINN bundle method that calculates error bounds without numerical solutions, improving the analysis of matter perturbations in cosmological models.

Findings

Achieved more stringent constraints on $\,\Omega_m-\sigma_8$ plane.

Provided error bounds on matter perturbation evolution without numerical solutions.

Validated the PINN approach against recent structure growth data.

Abstract

We consider the evolution of linear matter perturbations in the context of the standard cosmological model ($\Lambda$CDM) and a phenomenological modified gravity model. We use the physics-informed neural network (PINN) bundle method, which allows to integrate differential systems as an alternative to the traditional numerical method. We apply the PINN bundle method to the equation that describes the matter perturbation evolution, to compare its outcomes with recent data on structure growth, $f\sigma_8$. Unlike our previous works, we can calculate a bound on the error of this observable without using the numerical solution of the equation. For this, we use a method developed previously by ourselves to calculate an exact bound on the PINN-based solution using only the outcomes of the network and its residual. On the other hand, the use of an updated data set allows us to obtain more stringent constraints on the plane $\Omega_m-\sigma_8$ than previous works.