NF2 and physics-informed neural coronal extrapolation
NF2 represents the coronal magnetic field with a neural network and trains it using both boundary observations and force-free physics.
Instead of storing only on a grid, the model learns a continuous function:
where are the trainable network parameters. Once trained, the network itself is the magnetic-field representation.
The physics-informed idea
A physics-informed neural network puts equation residuals directly into the loss. For NLFFF extrapolation, the usual structure is:
The model is trained to:
- match the vector magnetogram at the lower boundary;
- reduce the force-free residual ;
- reduce the divergence residual .
Automatic differentiation supplies the spatial derivatives needed for curl and divergence. That is one of the main attractions of the neural-field representation: the derivatives come from the model directly, rather than from finite-difference stencils on a grid.
How to frame NF2
NF2 is not a black-box AI replacement for solar physics.
A cleaner description is:
NF2 is a neural representation and optimiser for a known physics-constrained NLFFF inverse problem.
That wording matters. The physics target is the same as in classical NLFFF extrapolation. The difference is the representation, the optimiser, and the way the boundary and residual terms are balanced during training.
Main caution
A low aggregate loss is not enough. The model can trade one objective against another:
- fit the magnetogram while leaving too much divergence;
- reduce divergence while drifting away from the boundary;
- become smooth and force-free while losing real active-region structure.
So the individual residuals and physical diagnostics have to be read separately, not only as one total training curve.