Neural Netowrk Differential Equation Plasma Equilibrium Solver

PyTorch implementation of Neural Netowrk Differential Equation Plasma Equilibrium Solver.

Equilibria

The implemented equilibria are described in physics.py:

• HighBetaEquilibrium: simplified high-beta tokamak;
• GradShafranovEquilibrium: fixed-boundary Grad-Shafranov tokamak;
• InverseGradShafranovEquilibrium: fixed-boundary inverse Grad-Shafranov 2D equilibrium;

Train

Define the equilibrium and training procedure arguments via a yaml configuration file:

python train.py --config=configs/solovev.yaml

Available configurations:

• configs/solovev.yaml: Solov'ev case as in Hirshman. The Physics of fluids 26.12 (1983): 3553-3568.
• configs/dshape.yaml: a D-shape tokamak equilibrium as in Dudt. Physics of Plasmas 27.10 (2020): 102513.
• configs/high_beta.yaml: high-beta case as in van Milligen. Physical review letters 75.20 (1995): 3594.
• configs/inverse_solovev.yaml: inverse Solov'ev tokamak equilibrium.
• configs/inverse_dshape.yaml: inverse D-shape tokamak equilibrium.

Test

To run all tests, simply run:

pytest

TODO

• fix equilibrium definition from VMEC wout (i.e., F function parsing)