Detection of magnetohydrodynamic waves by using convolutional neural networks

Nonlinear wave interactions in magnetohydrodynamic (MHD), such as shock refraction at an inclined density interface, lead to a plethora of wave patterns with numerous wave types. Identifying different types of MHD waves is an important and challenging task in such complex wave patterns. Owing to the multiplicity of solutions and their admissibility for different systems, the identification of MHD wave types is complicated if one relies on the Rankine-Hugoniot conditions. This paper proposes two MHD wave detection methods based on convolutional neural networks (CNN) to enable wave classification and identify their locations. The first method separates the output into regression (location prediction) and classification problems, assuming the number of waves for each training data is fixed. In contrast, the second method does not specify the number of waves {\it a priori} and the algorithm predicts wave locations and classifies types using only regression. We use one-dimensional (1D) input data (density, velocity and magnetic fields) to train the two models that successfully reproduce a complex two-dimensional (2D) MHD shock refraction structure. The first fixed output model efficiently provides high precision and recall, achieving total neural network accuracy up to $99\%$, and the classification accuracy of some waves approaches unity. The second detection model has relatively lower performance, with more sensitivity to the setting of parameters, such as the number of grid cells $N_{grid}$ and the thresholds of confidence score and class probability, etc. The proposed two methods demonstrate very strong potential for MHD wave detection in complex wave structures and interactions.