Data-driven discovery of sub-grid models for collisionless magnetic reconnection
Alexander Velberg
Massachussetts Institute of Technology
Nuclear Science and Engineering
Capturing the global effects of collisionless magnetic reconnection is a key challenge for modeling a variety of multi-scale laboratory and astrophysical plasma systems. In this work, we present a data-driven, machine learning approach to spatial sub-grid closure discovery and apply it to data from simulations of coalescing magnetic islands. The discovered closures capture the effects of collisionless reconnection on the large, magneto-hydrodynamic scale structures supplying the flux, enabling an accurate description of the timescale and rate of reconnection on a coarsened grid. Despite the opaque nature of the neural networks we use here, systematic application of constraints on the information available during training reveals that accurate closures require local gradients of the magnetic fields and flows. Finally, we investigate the relationship between these closures and a simple anomalous resistivity and viscosity, finding that our sub-grid closure for Ohm’s law is accurately represented by an anomalous hyper-resistivity at the reconnection X-point. Away from this point and in the case of viscosity, the additional complexity offered by the machine learned closures leads to significantly better performance.