Clarify train loss vs reported Rel-L2 (NASA-CRM / AhmedML / DrivAerML)

Hi — thanks for the paper and code. We're reimplementing the industrial benchmarks and want to match your training/eval protocol.

Context. Table 9 lists training Loss = Relative L2, Appendix A.3 says targets are standardized (zero mean / unit variance), and Table 4 reports per-field Rel-L2 (%). It's unclear how these interact, and the release doesn't fully cover NASA-CRM / field-wise metrics for every case.

For each of NASA-CRM, AhmedML, and DrivAerML, could you clarify:

Training loss

1. Is Rel-L2 applied in normalized space, physical space (after denorm), or is training actually MSE on normalized targets with Rel-L2 only used at eval?
2. Is the objective a single joint Rel-L2 over all output channels, or an average of per-field Rel-L2 (e.g. 0.5*(RelL2(cp)+RelL2(cf)))?
3. For vector fields, does the model predict components or magnitude?
   • NASA-CRM: [cp, cx, cy, cz] vs [cp, |cf|] with |cf|=√(cx²+cy²+cz²)?
   • AhmedML / DrivAerML surface: pressure ps + wall shear τ as a 3-vector or |τ|?
   • AhmedML / DrivAerML volume: velocity u as a 3-vector or |u|, plus volume pressure pv?
4. Any special field/channel weighting?

Reported metrics (Table 4 / App. A.3)

1. Always computed in physical units after inverse standardization?
2. For vector quantities (Cf, τ, u): Rel-L2 on the full vector, or on the per-node magnitude first?
3. Per-field Rel-L2 = mean over test samples of ‖ŷ−y‖₂ / ‖y‖₂ on that field only?
4. With amortized subset training (Ahmed/DrivAer), are metrics still on the full mesh?

A short answer per dataset (or a pointer to the loss/metric code) would be perfect. Thanks!

Start by locating the loss and metric implementations used for NASA-CRM, AhmedML, and DrivAerML, then compare them with the standardization and benchmark descriptions in Appendix A.3 and Table 4. Done means documenting the training-space, channel aggregation, vector handling, weighting, and full-mesh evaluation choices for each dataset, or linking to the relevant code.