Machine learning predictions of high Reynolds number rotating MHD turbulence

Machine learning has been used to predict the time evolution of complex systems. Here we investigate the predictability of a spherical Couette high Reynolds number MHD experiment, using a recurrent neural network technique called reservoir computing, an auto-regressive model, and a hybrid combination of these two methods. These methods do not use a physical model; they use only past measurements of the system to predict future measurements. We analyze how their performance changes with different amounts of training data, and different fluid dynamical states. We tested three different approaches to predict the time evolution of a nonlinear system, our Three-meter experiment, and found that the hybrid of the reservoir computer and the auto-regressive model outperforms each of its components, and is capable of predicting the time evolution for five magnetic dipole timescales with an accuracy higher than the average one time step fluctuation. We applied these techniques to experiments with different fluid dynamical states and demonstrated that some of the states are more predictable than others. We show that the hybrid model is also capable of predicting the long time climate of the system, and even while it might far from the real data in terms of the RMS error, it keeps converging on a trajectory in phase space that is very similar to what is has learned during the testing phase. We also discovered that for this system it is necessary to have more than ten dipole diffusion timescales of the spatially distributed training data in order to predict the dynamics; a comparable dataset is not currently available for the Earth's magnetic field.