Data-driven discovery of sub-grid models for a turbulent electromotive force in magnetic reconnection

Sub-grid closures are often employed to capture the effects of small-scale, kinetic physics on larger scales, reducing the need to resolve large scale separations. While there is no general prescription for discovering such models, recent advances in machine learning techniques may offer mechanisms for discovering closures directly from data. We present an approach to sub-grid closure discovery in which physics-informed constraints are applied to shallow, fully convolutional neural networks (FCNs), implicitly revealing information about the physics needed for closure. We apply this framework to the nonlinear, multi-scale dynamics of coalescing magnetic islands in a low-beta, strongly magnetized pair plasma. We derive a simple analytic expression for a turbulent emf (A) describing the feedback of electron inertia scale physics on coarse-grained, MHD-scale fields and show via a systematic reduction of the FCN receptive field that the dynamics encoded in A are accurately captured using only spatially local patches of the coarse-grained fields as inputs. To better understand the validity and generalizability of our results, we evaluate sensitivity to the specific coarse-graining procedure and assess performance on a variety of physically motivated metrics for multiple simulations at different scale-separations.