Asteroseismology of $\delta$ Scuti stars: emulating model grids using a neural network

Young $\delta$ Scuti stars have proven to be valuable asteroseismic targets but obtaining robust uncertainties on their inferred properties is challenging. We aim to quantify the random uncertainties in grid-based modelling of $\delta$ Sct stars. We apply Bayesian inference using nested sampling and a neural network emulator of stellar models, testing our method on both simulated and real stars. Based on results from simulated stars we demonstrate that our method can recover plausible posterior probability density estimates while accounting for both the random uncertainty from the observations and neural network emulation. We find that the posterior distributions of the fundamental parameters can be significantly non-Gaussian, multi-modal, and have strong covariance. We conclude that our method reliably estimates the random uncertainty in the modelling of $\delta$ Sct stars and paves the way for the investigation and quantification of the systematic uncertainty.