Detection of magnetohydrodynamic waves by using convolutional neural networks

Abstract

Nonlinear wave interactions in magnetohydrodynamics (MHD), such as shock refraction at an inclined density interface, lead to a plethora of wave patterns with numerous wave types. Identification of different types of MHD waves is an important and challenging task in such complex wave patterns. Moreover, owing to the multiplicity of solutions and their admissibility for different systems, especially for intermediate-type MHD shock waves, the identification of MHD wave types is complicated if one relies on the Rankine–Hugoniot jump conditions. MHD wave detection is further exacerbated by nonphysical smearing of discontinuous shock waves in numerical simulations. This paper proposes two MHD wave detection methods based on convolutional neural network 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 a priori, and the algorithm predicts wave locations and classifies types using only regression. We use one-dimensional input data (density, velocity, and magnetic fields) to train the two models that successfully reproduce a complex two-dimensional 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 low performance, with more sensitivity to the setting of parameters, such as the number of grid cells Ngrid and the thresholds of confidence score and class probability, etc. The detection model achieves better than 90% accuracy with F1 score >0.95. The proposed two methods demonstrate very strong potential for MHD wave detection in complex wave structures and interactions.