Supervised neural networks for helioseismic ring-diagram inversions

Context. The inversion of ring fit parameters to obtain subsurface flow maps in ring-diagram analysis for eight years of SDO observations is computationally expensive, requiring similar to 3200 CPU hours. Aims. In this paper we apply machine-learning techniques to the inversion step of the ring diagram pipeline in order to speed up the calculations. Specifically, we train a predictor for subsurface flows using the mode fit parameters and the previous inversion results to replace future inversion requirements. Methods. We utilize artificial neural networks (ANNs) as a supervised learning method for predicting the flows in 15 degrees ring tiles. We discuss each step of the proposed method to determine the optimal approach. In order 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. Results. The ANN 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 similar to 31 CPU hours. Initial training of the networks requires similar to 3 CPU hours. The trained ANN can achieve a rms 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. Conclusions. We show 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 10(-4) CPU hours for future predictions.