  Asteroseismology is a powerful tool that may be applied to shed light on
stellar interiors and stellar evolution. Mixed modes, behaving as acoustic
waves in the envelope and buoyancy modes in the core, are remarkable because
they allow for probing the radiative cores and evanescent zones of red-giant
stars. Here, we have developed a neural network that can accurately infer the
coupling strength, a parameter related to the size of the evanescent zone, of
solar-like stars in $\sim$5 milliseconds. In comparison with existing methods,
we found that only $\sim$43\% inferences were in agreement to within a
difference of 0.03 on a sample of $\sim$1,700 \textit{Kepler} red giants. To
understand the origin of these differences, we analyzed a few of these stars
using independent techniques such as the Monte Carlo Markov Chain method and
Echelle diagrams. Through our analysis, we discovered that these alternate
techniques are supportive of the neural-net inferences. We also demonstrate
that the network can be used to yield estimates of coupling strength and large
period separation in stars with structural discontinuities. Our findings
suggest that the rate of decline in the coupling strength in the red-giant
branch is greater than previously believed. These results are in closer
agreement with calculations of stellar-evolution models than prior estimates,
further underscoring the remarkable success of stellar-evolution theory and
computation. Additionally, we show that the uncertainty in measuring
large-period separation increases rapidly with diminishing coupling strength.
