Machine learning based scaling relations for mass, radius, and age of Solar-like oscillating stars

We investigate scaling relations for stellar mass, radius, and age in stars exhibiting solar-like oscillations using two observational data sets comprising 110 stars. Using data set 1 (80 stars), we derive empirical scaling relations incorporating asteroseismic parameters – the frequency of maximum oscillation power, large, and small frequency separations – alongside effective temperature and metallicity. To account for non-Gaussian uncertainties in the stellar parameters, we employ an ensemble machine learning approach that combines Ridge, Huber, and Gradient Boosting regressors to predict stellar mass, radius, and age, along with deriving the corresponding coefficients for the scaling relations. We assess coefficient uncertainties by combining jackknife and bootstrap resampling techniques. Using the resulting scaling relations, we predict the mass, radius, and age of 30 stars in data set 2. These predictions closely match observational data, even when the parameters slightly differ from those in the training set. The predicted stellar ages range from 2.29 to 10.09 Gyr, consistent with Solar-like oscillators. Our findings show that combining machine learning regression with resampling-based uncertainty estimation provides an effective and reliable approach for deriving scaling relations, offering valuable insights for stellar characterization in asteroseismic research.