NF2 diagnostics for physical credibility

NF2 should not be judged by field-line plots alone. A magnetic field can look plausible while still violating the physics that makes it useful.

The useful question is:

Does the reconstructed field behave like a credible coronal NLFFF field, not merely like a smooth picture?

Core checks

A good NF2 evaluation should ask:

1. Boundary agreement - does the model bottom boundary match the input SHARP vector magnetogram?
2. Divergence control - is $\nabla \cdot \mathbf{B}$ small, or is the model inventing magnetic sources and sinks?
3. Force-freeness - is $(\nabla \times \mathbf{B})\times \mathbf{B}$ small, meaning current is close to parallel with the field?
4. Magnetic energy - does the field contain credible free energy above a potential-field baseline?
5. Topology - do field lines, connectivity, current concentrations, and active-region structures make physical sense?
6. Reproducibility - can the result be repeated from documented data, configs, and checkpoints?

Main residuals

Force-free residual:

$${\mathbf{R}}_{\mathrm{ff}}=(\nabla \times \mathbf{B})\times \mathbf{B}.$$

Divergence residual:

$$R_{\mathrm{div}}=\nabla \cdot \mathbf{B}.$$

Boundary residual:

$${\mathbf{R}}_{\mathrm{b}}={\mathbf{B}}_{\mathrm{model}}(x,y,0)-{\mathbf{B}}_{\mathrm{obs}}(x,y).$$

These should be inspected separately. A low total loss can hide the fact that one term is doing badly while the others compensate.

Good dissertation framing

The strongest outcome is not “NF2 made a pretty field”. It is a structured comparison showing:

• which settings improve physical diagnostics;
• which settings mainly improve visual appearance;
• where the method is sensitive to boundary weights, loss scaling, or data preparation;
• whether NF2 beats a potential-field baseline in a physically meaningful way.

That framing keeps the project honest. Pretty loops are useful as a sanity check, but they are not the science.

Related

• NF2 and physics-informed neural coronal extrapolation
• Residuals in NF2 and PINNs
• Magnetic energy and free energy in active regions
• NOAA AR 11158 as an NF2 benchmark
• NLFFF quality metrics