Grassmann geometry for plasma turbulence surrogate models

Abstract

Predictive, fast reduced-order models are essential for fusion devices like ITER, where real-time transport forecasting, optimisation, and control cannot depend on costly first-principles turbulence simulations alone. We tackle this problem with the LaQuey Mahajan, Rutherford, and Tang equation, a reduced trapped-ion mode turbulence model equivalent, after nondimensionalisation, to the Kuramoto–Sivashinsky equation. We use a geometry-aware reduced-order framework over a two-parameter space of damping and dissipation. Local proper orthogonal decomposition bases extracted from direct numerical simulation are used to build Galerkin reduced models. Frozen bases remain accurate when turbulent structures vary smoothly, but they deviate near transitional regimes where fluctuation content reorganises. Grassmann-manifold analysis shows that subspace proximity does not always guarantee physical accuracy: transport may be reproduced even when fine-scale structure is not. Adaptive, parameter-dependent bases obtained by manifold interpolation significantly improve robustness and recover both large-scale and fine-scale fidelity. Overall, the results show that transport accuracy, structural fidelity, and basis geometry are complementary validation criteria for plasma surrogates, and they support efficient predictive models for ITER-scale optimisation and control.