arXiv subjects

Augusto T. Chantada

Publications and source records attributed to Augusto T. Chantada.

4 recordsLinked to original sources

arXiv2025

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

We consider the evolution of linear matter perturbations in the context of the standard cosmological model ($Λ$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, $fσ_8$. 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 $Ω_m-σ_8$ than previous works.

astro-ph.CO↗

arXiv2024

Exact and approximate error bounds for physics-informed neural networks

The use of neural networks to solve differential equations, as an alternative to traditional numerical solvers, has increased recently. However, error bounds for the obtained solutions have only been developed for certain equations. In this work, we report important progress in calculating error bounds of physics-informed neural networks (PINNs) solutions of nonlinear first-order ODEs. We give a general expression that describes the error of the solution that the PINN-based method provides for a nonlinear first-order ODE. In addition, we propose a technique to calculate an approximate bound for the general case and an exact bound for a particular case. The error bounds are computed using only the residual information and the equation structure. We apply the proposed methods to particular cases and show that they can successfully provide error bounds without relying on the numerical solution.

cs.LG↗

arXiv2024

Faster Bayesian inference with neural network bundles and new results for $f(R)$ models

In the last few years, there has been significant progress in the development of machine learning methods tailored to astrophysics and cosmology. We have recently applied one of these, namely, the neural network bundle method, to the cosmological scenario. Moreover, we showed that in some cases the computational times of the Bayesian inference process can be reduced. In this paper, we present an improvement to the neural network bundle method that results in a significant reduction of the computational times of the statistical analysis. The novel aspect consists of the use of the neural network bundle method to calculate the luminosity distance of type Ia supernovae, which is usually computed through an integral with numerical methods. In this work, we have applied this improvement to the Hu-Sawicki and Starobinsky $f(R)$ models. We also performed a statistical analysis with data from type Ia supernovae of the Pantheon+ compilation and cosmic chronometers. Another original aspect of this work is the different treatment we provide for the absolute magnitude of type Ia supernovae during the inference process, which results in different estimates of the distortion parameter than the ones obtained in the literature. We show that the statistical analyses carried out with our new method require lower computational times than the ones performed with both the numerical and the neural network method from our previous work. This reduction in time is more significant in the case of a difficult computational problem such as the ones addressed in this work.

astro-ph.CO↗

arXiv2023

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

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 $Λ\mathrm{CDM}$, 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 $\sim1\%$ 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.

astro-ph.CO↗