NN bundle method applied to cosmology: an improvement in computational times

In the last few years, there has been significant progress in the development of machine learning methods tailored to astrophysics and cosmology. Among the various methods that have been developed, there is one that allows to obtain a bundle of solutions of differential systems without the need of using traditional numerical solvers. We have recently applied this to the cosmological scenario and showed that in some cases the computational times of the 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 novelty of the method consists in 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 Starobinsky $f(R)$ model, which is more difficult to integrate than the $f(R)$ models analyzed in our previous work. We performed a statistical analysis with data from type Ia supernovae of the Pantheon+ compilation and cosmic chronometers to estimate the values of the free parameters of the Starobinsky model. 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 one we address in this work.