Machine-Learned Turbulence Closures
Neural closures replace unresolved turbulent fluxes in reduced plasma models, capturing effects that would otherwise require expensive kinetic simulation.
The closure problem
Plasma transport is dominated by small-scale turbulence driven by temperature and density gradients. Fluid or reduced models cannot resolve these scales, so they need a closure: a rule that expresses the turbulent flux in terms of the resolved fields. Deriving accurate analytic closures is hard because turbulence is nonlinear, non-local, and stiff.
Learning the closure
A machine-learned closure trains a network to predict the turbulent particle, heat, and momentum fluxes from local gradients, magnetic geometry, and collisionality, using high-fidelity gyrokinetic simulations as the training source. The network becomes a fast stand-in for the turbulence physics inside a transport solver.
Design choices
- Inputs: normalized gradients (a/L_T, a/L_n), safety factor, magnetic shear, collisionality, and ratios like T_i/T_e
- Outputs: heat and particle diffusivities or the fluxes themselves
- Constraints: enforce zero flux below the linear instability threshold to respect known physics
A recurring difficulty is the threshold: turbulent transport switches on sharply once a critical gradient is exceeded. Networks that ignore this produce spurious flux in stable regions. Building the threshold into the model, or training densely near it, is essential for stable coupled simulations.
Coupling and stability
Once embedded in a transport solver, a learned closure is called thousands of times as profiles evolve. Small prediction errors can amplify, so closures must be smooth and monotone where physics demands. Techniques include enforcing non-negativity of diffusivities and clipping outputs to physically plausible ranges.
Learned closures make it practical to simulate the temperature and density profiles of a device across many operating points, which supports scenario design for concepts like the Hyperion breeder. They accelerate but do not replace gyrokinetics; the closure is only as trustworthy as the simulation dataset it learned from, so validation against fresh high-fidelity runs is standard.