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Cosmological informed neural networks to solve the background dynamics of the Universe

Augusto T. ChantadaSusana J. LandauPavlos ProtopapasClaudia G. Sc\'occolaCecilia Garraffo
May 2022
The field of machine learning has drawn increasing interest from variousother fields due to the success of its methods at solving a plethora ofdifferent problems. An application of these has been to train artificial neuralnetworks to solve differential equations without the need of a numericalsolver. This particular application offers an alternative to conventionalnumerical methods, with advantages such as lower memory required to store thesolutions, parallelization, and in some cases less overall computational costthan its numerical counterparts. In this work, we train artificial neuralnetworks to represent a bundle of solutions of the differential equations thatgovern the background dynamics of the Universe for four different models. Themodels we have chosen are $\Lambda \mathrm{CDM}$, theChevallier-Polarski-Linder parametric dark energy model, a quintessence modelwith an exponential potential, and the Hu-Sawicki $f\left(R\right)$ model. Weused the solutions that the networks provide to perform statistical analyses toestimate the values of each model's parameters with observational data; namely,estimates of the Hubble parameter from Cosmic Chronometers, the Supernovae typeIa data from the Pantheon compilation, and measurements from Baryon AcousticOscillations. The results we obtain for all models match similar estimationsdone in the literature using numerical solvers. In addition, we estimated theerror of the solutions by comparing them to the analytical solution when thereis one, or to a high-precision numerical solution when there is not. Throughthose estimations we found that the error of the solutions was at most$\sim1\%$ in the region of the parameter space that concerns the $95\%$confidence regions that we found using the data, for all models and allstatistical analyses performed in this work.