Inferring Cosmological Parameters with Evidential Physics-Informed Neural Networks

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 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 ΛCDM, wCDM and ΛsCDM models. Unlike previous results arising from the standard approach of minimizing an appropriate χ2 function, the posterior distributions for parameters in various models trained purely on Pantheon+ data were found to be largely contained within the 2σ contours of their counterparts trained on BAO data. Our study illustrates how a data-driven machine learning approach can be suitably adapted for cosmological parameter inference.