Asteroseismology of solar-like oscillators: emulating individual mode frequencies with a branching neural network

Accurately measuring stellar ages and internal structures is challenging, but the inclusion of asteroseismic observables can substantially improve precision. However, the curse of dimensionality means this comes at a high computational cost when using standard interpolation methods across grids of stellar models. Furthermore, without a rigorous treatment of random uncertainties in grid-based modelling, it is not possible to address systematic errors in stellar models. We present PITCHFORK -- a multilayer perceptron neural network with a branching architecture capable of rapid emulation of both classical stellar observables and individual asteroseismic oscillation modes of solar-like oscillators. PITCHFORK can predict the classical observables $T_{\text{eff}}$, $L$, and $\left[\mathrm{Fe}/\mathrm{H}\right]$ with precisions of $5.88\,\text{K}$, $0.014\,\text{L}_{\odot}$, and $0.001\,\text{dex}$, respectively, and can predict 35 individual radial mode frequencies with a uniform precision of $0.02$ per cent. PITCHFORK is coupled to a vectorised Bayesian inference pipeline to return well-sampled and fully marginalised posterior distributions. We validate our rigorous treatment of the random uncertainties -- including the asteroseismic surface effect -- in an extensive hare-and-hounds exercise. We also demonstrate our ability to infer the stellar properties of benchmark stars -- namely, the Sun and the binary stars 16 Cygni A and B. This work demonstrates a computationally scalable and statistically robust framework for stellar parameter inference of solar-like oscillators using individual asteroseismic mode frequencies. This provides a foundation for the treatment of systematics in preparation for the imminent abundance of asteroseismic data from future missions.