PINNferring the Hubble Function with Uncertainties

TL;DR

This paper introduces a physics-informed neural network approach to efficiently reconstruct the Hubble function from supernova data, incorporating uncertainty quantification for cosmological analysis.

Contribution

It presents a novel PINN-based emulator for the Hubble function that is model-independent, parameter-free, and includes a new uncertainty estimation method.

Findings

Accurate reconstruction of the Hubble function from supernova data.

Effective uncertainty quantification using heteroscedastic loss and ensembles.

Fast predictions enabling real-time cosmological data analysis.

Abstract

The Hubble function characterizes a given Friedmann-Robertson-Walker spacetime and can be related to the densities of the cosmological fluids and their equations of state. We show how physics-informed neural networks (PINNs) emulate this dynamical system and provide fast predictions of the luminosity distance for a given choice of densities and equations of state, as needed for the analysis of supernova data. We use this emulator to perform a model-independent and parameter-free reconstruction of the Hubble function on the basis of supernova data. As part of this study, we develop and validate an uncertainty treatment for PINNs using a heteroscedastic loss and repulsive ensembles.