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Plasmas are highly nonlinear and multi-scale, motivating a hierarchy ofmodels to understand and describe their behavior. However, there is a scarcityof plasma models of lower fidelity than magnetohydrodynamics (MHD). Galerkinmodels, obtained by projection of the MHD equations onto a truncated modalbasis, can furnish this gap in the lower levels of the model hierarchy. In thepresent work, we develop low-dimensional Galerkin plasma models which preserveglobal conservation laws by construction. This additional model structureenables physics-constrained machine learning algorithms that can discover thesetypes of low-dimensional plasma models directly from data. This formulationrelies on an energy-based inner product which takes into account all of thedynamic variables. The theoretical results here build a bridge to the extensiveGalerkin literature in fluid mechanics, and facilitate the development ofphysics-constrained reduced-order models from plasma data.

The structure of global conservation laws in Galerkin plasma models