  Nonlinear wave interactions, such as shock refraction at an inclined density
interface, in magnetohydrodynamic (MHD) lead to a plethora of wave patterns
with myriad 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 solely relies on the Rankine-Hugoniot jump
conditions. MHD wave detection is further exacerbated by the unphysical
smearing of discontinuous shock waves in numerical simulations. We present two
MHD wave detection methods based on a convolutional neural network (CNN) which
enables the classification of waves and identification of their locations. The
first method separates the output into a regression (location prediction) and a
classification problem assuming the number of waves for each training data is
fixed. In the second method, the number of waves is not specified a priori and
the algorithm, using only regression, predicts the waves' locations and
classifies their types. The first fixed output model efficiently provides high
precision and recall, the accuracy of the entire neural network achieved is up
to 0.99, 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 to be applied for MHD wave detection
in some complex wave structures and interactions.
