Self-Consistent Physics-Informed Surrogates for Direct and Inverse Tokamak Equilibria

F. Galfrascoli, Z. Wang, E. Schuster

68th Division of Plasma Physics (DPP) Annual Meeting of the American Physical Society (APS)

Chicago, IL, USA, November 2-6, 2026

Iterative free-boundary equilibrium solvers can be prohibitively expensive for applications requiring large numbers of tokamak equilibrium evaluations. To address this limitation, physics-informed neural-network surrogates have been developed for both the forward and inverse equilibrium problems. The forward mapping determines the poloidal magnetic-flux distribution from poloidal-field coil currents, whereas the inverse mapping identifies coil currents associated with a specified plasma boundary. Equilibrium solutions generated by the Control-Oriented Tokamak Equilibrium Solver (COTES) are used for training. Rather than relying exclusively on supervised data, the training formulation incorporates a discrete Grad--Shafranov equation constructed from the finite-difference operator of the original solver. The source distribution entering this equation is evaluated from the flux predicted by each network, coupling the magnetic-flux solution, the corresponding toroidal current density, and the equilibrium operator. This formulation improves the physical consistency of both surrogate mappings without introducing nonlinear free-boundary iterations during inference. The resulting models support rapid repeated calculations for parameter exploration, optimization, simulation, and plasma-control applications. On a CPU, each equilibrium is evaluated in less than one millisecond, reducing computational cost by more than three orders of magnitude relative to the iterative solver.

*Supported by the US DOE under DE-SC0010661.