  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.
