Distribution and Evolution of Chorus Waves Modeled by a Neural Network: The Importance of Imbalanced Regression

Whistler-mode chorus waves play an essential role in the acceleration and loss of energetic electrons in the Earth's inner magnetosphere, with the more intense waves producing the most dramatic effects. However, it is challenging to predict the amplitude of strong chorus waves due to the imbalanced nature of the dataset, i.e., there are many more non-chorus data points than strong chorus waves. Thus, traditional models usually underestimate chorus wave amplitudes significantly during active times. Using an imbalanced regressive method, we develop a neural network model of the lower-band (LB) chorus waves using over 13 satellite-year observations from the EMFISIS instrument onboard two Van Allen Probes. A feature selection process is carried out, which suggests that the auroral electrojet index captures most of the variations of chorus waves. The large amplitude of strong chorus waves can be predicted for the first time. Furthermore, our model shows that the equatorial LB chorus's spatiotemporal evolution is similar to the drift path of substorm-injected electrons. We also show that the chorus waves have a peak amplitude at the equator in the source MLT near midnight, but toward noon, there is a local minimum in amplitude at the equator with two off-equator amplitude peaks in both hemispheres, which is likely caused by the bifurcated drift paths of the substorm injections due to bifurcation of the magnetic field minima on the dayside. Since data imbalance is ubiquitous and inherent in space physics and other physical systems, imbalanced regressive methods deserve more attention in space physics.