  The inversion of ring fit parameters to obtain subsurface flow maps in
ring-diagram analysis for 8 years of SDO observations is computationally
expensive, requiring ~3200 CPU hours. In this paper we apply machine learning
techniques to the inversion in order to speed up calculations. Specifically, we
train a predictor for subsurface flows using the mode fit parameters and the
previous inversion results, to replace future inversion requirements. We
utilize Artificial Neural Networks as a supervised learning method for
predicting the flows in 15 degree ring tiles. To demonstrate that the machine
learning results still contain the subtle signatures key to local helioseismic
studies, we use the machine learning results to study the recently discovered
solar equatorial Rossby waves. The Artificial Neural Network is computationally
efficient, able to make future flow predictions of an entire Carrington
rotation in a matter of seconds, which is much faster than the current ~31 CPU
hours. Initial training of the networks requires ~3 CPU hours. The trained
Artificial Neural Network can achieve a root mean-square error equal to
approximately half that reported for the velocity inversions, demonstrating the
accuracy of the machine learning (and perhaps the overestimation of the
original errors from the ring-diagram pipeline). We find the signature of
equatorial Rossby waves in the machine learning flows covering six years of
data, demonstrating that small-amplitude signals are maintained. The recovery
of Rossby waves in the machine learning flow maps can be achieved with only one
Carrington rotation (27.275 days) of training data. We have shown that machine
learning can be applied to, and perform more efficiently than the current
ring-diagram inversion. The computation burden of the machine learning includes
3 CPU hours for initial training, then around 0.0001 CPU hours for future
predictions.
