Inferring Cosmological Parameters with Evidential Physics-Informed Neural Networks
This work addresses cosmological parameter inference for astrophysicists, offering a machine learning-based alternative to traditional methods, but it is incremental as it builds on existing techniques.
The paper tackles the problem of predicting cosmological parameters from supernovae and baryon acoustic oscillations datasets using a novel machine learning framework, resulting in posterior distributions for parameters that are largely contained within 2σ contours and Hubble tension estimates within about 2σ of each other.
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 $Λ$CDM, $w$CDM and $Λ_s$CDM models. Unlike previous results arising from the standard approach of minimizing an appropriate $χ^2$ 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. Their posterior medians for $h_0$ were within about $2σ$ of one another, indicating that our machine learning-guided approach provides a different measure of the Hubble tension.