Learning magnetohydrodynamics from numerical turbulence with sparse regression

We demonstrate that all governing equations of magnetohydrodynamics can be accurately recovered from 3D MHD turbulence simulations using machine-learning algorithms that exploit the weak formulation of the equations and scalable sparse regression. The weak formulation is especially powerful for conservative equations that arise in hydrodynamics. Our scalable sparse regression places all equations on equal footing: dynamical equations and spatial constraints are both discovered. We investigate scaling of coefficient error with weak form hyperparameters and offer heuristics for accurate equation recovery. We then discuss the utility of our approach in discovering closure relations for MHD turbulence.