Independent initial fields evolve under the same viscosity. The comparison also separates relational training from extra prediction updates.
3 distributionsID, viscous OOD, inviscid OOD
Motion preview
Burgers field trajectoryBurgers data: Zituo Chen · CC BY 4.0 · redrawn with RdBu_r. Source & changes
Across independent experiences
What persists.
Viscosity ν.
Across distinct realizations
What changes.
Independent initial fields.
Experience → prediction
The task.
Independent trajectory + recipient field.
→ One-dimensional field evolution.
Evaluated instance
The comparison.
Released NOD · relation-trained stage, then prediction-only continuation.
Controls. Released-default NOD; Random; continued NOD.
Interpreting the evidence
What stays fixed in the test.
One fixed SPRII continuation recipe is used across ID, viscous OOD and inviscid OOD. Viscosity probes and frozen-predictor donor interventions are measured at the same checkpoints.
What this setting establishes.
The fixed continuation endpoint has lower mean error than released-default NOD in all three distributions. Added-update controls are reported separately.
Scope of the evidence
Extra prediction updates matter: continued NOD has slightly lower OOD means than the SPRII continuation in the matched-update comparison. The displayed field is a released training trajectory, not a model prediction.
Full result record
Measurements and comparisons.
Reported results are kept with their own populations and conditions. Development, held-out and sealed comparisons remain separate.
01 / Study Table 1
Native Burgers prediction
Released manifest; 3 source seeds
Trajectory MSE × 10⁻³ ↓
Native Burgers prediction
Method
ID
Viscous OOD
Inviscid OOD
Released-default NOD
9.096 ± .544
8.012 ± .815
11.857 ± .628
SPRII (fixed continuation endpoint)
8.999 ± .798
7.487 ± .183
11.510 ± .360
BBold identifies the fixed SPRII endpoint in the released-default comparison.
SPRII (fixed continuation endpoint)The endpoint includes extra prediction updates. Continued NOD has slightly lower OOD means under the matched-update comparison.
Means ± source SD. SPRII includes prediction-only continuation; released-default NOD has no added updates. In the matched-update control, continued NOD has slightly lower mean OOD errors: 7.408 and 11.488, versus SPRII’s 7.487 and 11.510.
02 / Study Table 9
Burgers prediction with added-update controls
Sources 1234/5678/9012; released ID, viscous OOD and inviscid OOD
Native trajectory MSE × 10⁻³ ↓
Burgers prediction with added-update controls
Group
Track
ID
Viscous OOD
Inviscid OOD
Primary comparison
Released-default NOD
9.096 ± 0.544
8.012 ± 0.815
11.857 ± 0.628
Primary comparison
SPRII fixed endpoint
8.999 ± 0.798
7.487 ± 0.183
11.510 ± 0.360
Matched additional-update controls
Continued NOD
9.379 ± 0.340
7.408 ± 0.130
11.488 ± 0.215
Matched additional-update controls
Random continuation
9.538 (–)
8.900 (–)
11.503 (–)
BBold marks SPRII’s ID mean and continued NOD’s lower OOD means in the matched-update comparison.
The dashed rule separates the primary reference from the added-update controls.
Primary comparisonThe same SPRII endpoint is compared against continued NOD below. Three-source paired intervals for the released-default differences include zero.
Means ± sample SD over three sources; Random’s source SD was not supplied. SPRII-minus-released-default paired-source 95% t intervals (MSE ×10⁻³; n=3, df=2) are ID [−2.472,2.277], viscous OOD [−2.982,1.932], and inviscid OOD [−2.783,2.091]. Continued NOD has slightly lower OOD means under matched added updates.
03 / Study Table 10
Burgers accessibility and fixed-predictor donor use — A. Organization and accessibility
Same 3 continuation checkpoints; donor assay: 11-system truth bank
B/W ratio; viscosity probe R²; wrong-minus-matched relative-L₂ error at H50
Burgers accessibility and fixed-predictor donor use — A. Organization and accessibility
Track
Train B/W
ID R^2
Viscous-OOD R^2
Continued NOD
42.07 ± 14.74
0.924 ± 0.006
0.975 ± 0.004
SPRII fixed endpoint
24.58 ± 8.62
0.762 ± 0.141
0.895 ± 0.116
BBold marks the higher viscosity-probe means of continued NOD.
Continued NODAccessibility and prediction rankings need not agree; the B/W statistic is a separate measure of organization.
Means ± source SD at the same continuation checkpoints used for prediction. B/W uses each model’s training-standardized latent distances. Ridge probes fit training data only; ID and viscous OOD are separate populations. Accessibility does not establish predictive use.
04 / Study Table 10
Burgers accessibility and fixed-predictor donor use — B. Fixed-predictor donor substitution
Same 3 continuation checkpoints; donor assay: 11-system truth bank
B/W ratio; viscosity probe R²; wrong-minus-matched relative-L₂ error at H50
Burgers accessibility and fixed-predictor donor use — B. Fixed-predictor donor substitution
Track
H=50 penalty
95% interval
Continued NOD
0.13310
[0.06729,0.21265]
SPRII fixed endpoint
0.12753
[0.06538,0.20405]
BBold marks each model’s own wrong-donor penalty, not a ranking between penalties.
Continued NODPositive penalties show donor dependence through each fixed predictor. Only three source fits contribute to the descriptive intervals.
Donor substitution holds each predictor fixed. H50 wrong-minus-matched relative-L₂ intervals use 5,000 source/system bootstrap draws from the 11-system truth bank after averaging recipient cases. These descriptive intervals have only three fitted sources.