  With the observations of an unprecedented number of oscillating subgiant
stars expected from NASA's TESS mission, the asteroseismic characterization of
subgiant stars will be a vital task for stellar population studies and for
testing our theories of stellar evolution. To determine the fundamental
properties of a large sample of subgiant stars efficiently, we developed a deep
learning method that estimates distributions of fundamental parameters like age
and mass over a wide range of input physics by learning from a grid of stellar
models varied in eight physical parameters. We applied our method to four
Kepler subgiant stars and compare our results with previously determined
estimates. Our results show good agreement with previous estimates for three of
them (KIC 11026764, KIC 10920273, KIC 11395018). With the ability to explore a
vast range of stellar parameters, we determine that the remaining star, KIC
10005473, is likely to have an age 1 Gyr younger than its previously determined
estimate. Our method also estimates the efficiency of overshooting,
undershooting, and microscopic diffusion processes, from which we determined
that the parameters governing such processes are generally poorly-constrained
in subgiant models. We further demonstrate our method's utility for ensemble
asteroseismology by characterizing a sample of 30 Kepler subgiant stars, where
we find a majority of our age, mass, and radius estimates agree within
uncertainties from more computationally expensive grid-based modelling
techniques.
