Narrow Operator Models of Stellarator Equilibria in Fourier Zernike Basis
This provides a novel numerical approach for stellarator optimization, enabling efficient exploration of equilibrium variations for fusion energy research, though it is incremental in applying ML to a specific computational bottleneck.
The paper tackled the problem of computing a continuous distribution of ideal MHD equilibria in stellarators by varying only the pressure invariant, using multilayer perceptrons to map parameters to a Fourier Zernike basis, achieving a method that minimizes force residuals as implemented in the DESC solver.
Numerical computation of the ideal Magnetohydrodynamic (MHD) equilibrium magnetic field is at the base of stellarator optimisation and provides the starting point for solving more sophisticated Partial Differential Equations (PDEs) like transport or turbulence models. Conventional approaches solve for a single stationary point of the ideal MHD equations, which is fully defined by three invariants and the numerical scheme employed by the solver. We present the first numerical approach that can solve for a continuous distribution of equilibria with fixed boundary and rotational transform, varying only the pressure invariant. This approach minimises the force residual by optimising parameters of multilayer perceptrons (MLP) that map from a scalar pressure multiplier to the Fourier Zernike basis as implemented in the modern stellarator equilibrium solver DESC.