Equilibrium Reconstruction with Neural Networks
Learning fast approximations to the Grad-Shafranov solution that maps magnetic measurements to plasma shape and current.
The equilibrium problem
A tokamak plasma sits in force balance described by the Grad-Shafranov equation. Reconstruction infers the internal magnetic geometry (flux surfaces, plasma boundary, current profile) from external magnetic measurements and other diagnostics. Classic codes solve this iteratively, which can be too slow for real-time control at high rate.
Where ML helps
Neural networks trained on many solved equilibria learn a direct map from measurements to the reconstructed quantities. Once trained, inference is a fixed, fast forward pass, enabling reconstruction at control-loop rates. The training data come from the physics solver itself, so the network emulates a trusted code.
- Inputs: magnetic probe and flux-loop signals, coil currents, pressure constraints
- Outputs: boundary shape, flux map, plasma current profile, key scalars
- Benefit: constant-time inference suitable for real-time use
Keeping it physical
A purely data-driven map can violate force balance. Hybrid approaches use the network to initialize or accelerate the iterative solver, or add a physics residual to the training loss, so outputs stay close to true Grad-Shafranov solutions while remaining fast.
Validation
Learned reconstructions are validated against the full solver on held-out equilibria and against independent diagnostics where available. Error should be reported per quantity (boundary position, safety factor, stored energy) because a good average can hide a poor boundary near sensitive regions.
Design note
Fast reconstruction supports shape and position control studies for tokamak designs, including spherical tokamaks such as the Kronos breeder, where negative triangularity and a compact geometry make accurate boundary tracking important. All such work here is on simulated equilibria for a design, not measured plasmas.