Inferring Cosmological Parameters with Evidential Physics-Informed Neural Networks

Abstract: We examine the use of a novel variant of Physics-Informed Neural Networks to predict cosmological parameters from recent supernovae and baryon acoustic oscillations (BAO) datasets. Our machine learning framework generates uncertainty estimates for target variables and the inferred unknown parameters of the underlying PDE descriptions. Built upon a hybrid of the principles of Evidential Deep Learning, Physics-Informed Neural Networks, Bayesian Neural Networks and Gaussian Processes, our model enables learning of the posterior distribution of the unknown PDE parameters through standard gradient-descent based training. We apply our model to an up-to-date BAO dataset (Bousis et al. 2024) calibrated with the CMB-inferred sound horizon, and the Pantheon$+$ Sne Ia distances (Scolnic et al. 2018), examining the relative effectiveness and mutual consistency among the standard $\Lambda$CDM, $w$CDM and $\Lambda_s$CDM models. Unlike previous results arising from the standard approach of minimizing an appropriate $\chi^2$ function, the posterior distributions for parameters in various models trained purely on Pantheon$+$ data were found to be largely contained within the $2\sigma$ contours of their counterparts trained on BAO data. Their posterior medians for $h_0$ were within about $2\sigma$ of one another, indicating that our machine learning-guided approach provides a different measure of the Hubble tension.