Constraining stellar evolution theory with asteroseismology of $gamma$ Doradus stars using deep learning

The efficiency of the transport of angular momentum and chemical elements inside intermediate-mass stars lacks proper calibration, thereby introducing uncertainties on a stars evolutionary pathway. Improvements require better estimation of stellar masses, evolutionary stages, and internal mixing properties. We aim to develop a neural network approach for asteroseismic modelling and test its capacity to provide stellar masses, ages, and overshooting parameter for a sample of 37 $gamma$ Doradus stars. Here, our goal is to perform the parameter estimation from modelling of individual periods measured for dipole modes with consecutive radial order. We have trained neural networks to predict theoretical pulsation periods of high-order gravity modes as well as the luminosity, effective temperature, and surface gravity for a given mass, age, overshooting parameter, diffusive envelope mixing, metallicity, and near-core rotation frequency. We have applied our neural networks for Computing Pulsation Periods and Photospheric Observables, C-3PO, to our sample and compute grids of stellar pulsation models for the estimated parameters. We present the near-core rotation rates (from literature) as a function of the inferred stellar age and critical rotation rate. We assess the rotation rates of the sample near the start of the main sequence assuming rigid rotation. Furthermore, we measure the extent of the core overshoot region and find no correlation with mass, age, or rotation. The neural network approach developed in this study allows for the derivation of stellar properties dominant for stellar evolution -- such as mass, age, and extent of core-boundary mixing. It also opens a path for future estimation of mixing profiles throughout the radiative envelope, with the aim to infer those profiles for large samples of $gamma$ Doradus stars.