All four sealed deliveries complete.800 train /100 validation /100 independent test.6000 actual updates,20 equal training cases per update,150 train passes. Validation-only checkpoint selection; original FP64 test targets and raw negative VM retained.
| Method | Active parameters | U mean / worst (%) | VM mean / worst (%) | Negative VM cases | Validation-selected update |
|---|---|---|---|---|---|
| TS3 | 982884 | 1.9533 / 9.3247 | 3.9167 / 8.3557 | 0 | 5800 |
| MGN | 985540 | 2.2391 / 4.8344 | 2.9398 / 5.4596 | 2 | 5900 |
| FNO | 984668 | 16.6537 / 45.3300 | 12.0373 / 58.1189 | 46 | 5900 |
| GNOT | 982170 | 2.5551 / 5.0302 | 8.7958 / 11.5641 | 6 | 6000 |
TS3 has the lowest mean test U error (1.9533%) and no negative-VM test cases. Its worst U error (9.3247%) is higher than MGN (4.8344%) and GNOT (5.0302%); mean accuracy and worst-case accuracy give different rankings.
MGN has the lowest mean and worst test VM errors (2.9398% and5.4596%) and the lowest worst test U error (4.8344%). Two cases still have raw negative VM; low relative error alone does not guarantee physical nonnegativity.
GNOT test U is2.5551% mean /5.0302% worst; test VM is8.7958% mean /11.5641% worst, with6 negative-VM cases. It improves over FNO on these U/VM metrics but has higher mean U and VM errors than TS3 and MGN in this fixed setup. Its worst U is lower than TS3, so it is not worse on every criterion.
FNO has the largest mean and worst U/VM errors among these four models and46 negative-VM test cases. This specific fixed logical-grid FNO result should not be generalized to all Fourier-operator formulations.
None meets U and VM <=1% on every one of the100 test cases. All four used the same800/100/100 split, seed20261029, original56 inputs/4 outputs,48977 native nodes, train800-only scales and6000 AdamW updates with20 equal cases per update (150 train passes). Only validation selected checkpoints; test predictions were evaluated after training and selection. These are single-seed fixed-budget results for the specified geometry/linear-FE family, not universal causal conclusions or production eligibility.
Exact comparison CSV | SHA evidence and conclusions | Separate TRAIN20 six-method comparison