Generality · Formation

NOD · FHN

Persistent parameters in a spatial world.

Reaction parameters shape two evolving fields. Multiple histories provide another way to aggregate evidence about the system.

2D fieldsprediction and parameter accessibility

Motion preview

FitzHugh–Nagumo field evolutionBased on Zituo Chen’s DR2D generator · Python solver illustration. Source & changes

Across independent experiences

What persists.

Reaction parameters (k, β).

Across distinct realizations

What changes.

Independent initial two-dimensional fields.

Experience → prediction

The task.

Independent field histories + recipient field.

→ Coupled u/v field evolution.

Evaluated instance

The comparison.

NOD-Hier · Align, then prediction-only adaptation.

Controls. Equal-history comparisons with NOD.

Interpreting the evidence

What stays fixed in the test.

History budgets are compared with equal-history NOD. The numerical solver, grid and integration convention are explicitly specified.

What this setting establishes.

The extension measures native field prediction, multi-history aggregation and reaction-factor accessibility separately.

Scope of the evidence

The missing original initial-condition bank was regenerated. These are reproducible Python simulations, not the authors’ exact initial-condition bank; the displayed trajectory is illustrative.

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 39

Complete follow-up outcomes

Separate configurations and populations shown row by row

MSE ↓, except FHN relative L₂ ↓

Complete follow-up outcomes
Configuration	Coverage	Numerical comparison	Finding / scope
JEPA Collision: J2	1,994 test episodes; 3 J2 seeds, 1/control	J2 0.184110 ± 0.005443; Structure 0.214314	Matched-only retest. Four arms and fixed-model interval: Table tab:jepa-collision-followup.
CoPhyNet Collision: Cross	4,000 development recipients; seed 0	Cross 0.203240; prior SPRII 0.210671	Near Native; paired interval against Native includes zero.
CPC Balls: Align	2,000 development recipients; seed 0	Align 1.392711; prior SPRII 1.415352; Structure 1.387643	Lower than prior SPRII, higher than Structure. Full contrasts are indexed in the package.
FHN: tuned SPRII	Report ICs 15/24/45; source 42; selection IC 5 excluded	ID K=4,H=50: SPRII 0.020132; extra-50k NOD 0.021522	Paired-system interval includes zero; other eight split/horizon cells have higher error. Extra-budget control.
Poke object-only: R8 / G2	400 development systems; source 0, reader 0; H=16	R8: M2 0.901091; M1 0.902588; recipient-only 0.911791. M2-M1: -0.001497 [-0.011855,0.008400]. G2: M2 0.913197; M1 0.908531; recipient-only 0.908021	Four-dimensional object-state error; M1 and M2 selected independently.
CoPhyNet Blocktower	8,088 development recipients; seed 0	SPRII 0.088180; Native/Structure 0.087114; Random 0.086230. SPRII-Random: 0.001951 [0.000668,0.003184]	Paired interval versus Structure includes zero; Random has lower mean error.

Bold identifies each follow-up configuration; heterogeneous numerical cells are deliberately not ranked.

Dashed rules separate experiments with different populations and fitted-model coverage.

All completed follow-ups from the configuration round are retained, including null and adverse results. Each row has its own population and model coverage. Paired intervals condition on the reported fitted models; the one-source development rows do not replace the original multi-source comparisons.

02 / Study Table 42

Equal-history aggregation in two-dimensional dynamics

Sources 42/43/44; report initial conditions 15/24/45; equal K for both methods

H50 relative L₂ error ↓; K1-to-K4 reduction ↑

Equal-history aggregation in two-dimensional dynamics
Split	SPRII reduction K1→K4	NOD reduction K1→K4	NOD K1	NOD K4	SPRII K1	SPRII K4
ID	16.9%	8.4%	0.02388	0.02188	0.02728	0.02266
OOD-Intra	18.0%	9.2%	0.02336	0.02121	0.02627	0.02155
OOD-Extra	10.9%	7.1%	0.03233	0.03002	0.03418	0.03046

Bold juxtaposes SPRII’s history-aggregation gain with NOD’s lower matched-K4 error.

IDWithin-model K1→K4 reduction and between-model K4 error answer different questions. NOD also has lower means at K1.

Both methods receive the same K independent histories. Means use three sources and report initial conditions 15/24/45; the unavailable original bank was regenerated. More histories reduce SPRII error, while NOD retains lower mean error in every listed equal-history cell.

03 / Study Table 43

FHN physical-factor accessibility — A. k

Sources 42/43/44; ID, OOD-Intra and OOD-Extra kept separate

Training-fitted K1 factor probe R² ↑

FHN physical-factor accessibility — A. k
Split	Method	Src 42	Src 43	Src 44
ID	NOD	0.9698	0.9301	0.9836
ID	SPRII	0.9444	0.3775	0.8952
Intra	NOD	0.9269	0.8098	0.9377
Intra	SPRII	0.8602	0.5513	0.6923
Extra	NOD	0.9351	0.9139	0.9284
Extra	SPRII	0.8587	0.0949	0.8730

Bold marks the higher k-probe R² within each matched split × source comparison.

Dashed rules separate evaluation splits.

ID · NODThese are factor-accessibility results; source-wise variation is not pooled into a prediction claim.

Training-fitted K1 probes measure k accessibility separately by source and split. These factor-readout measurements do not establish fixed-predictor use or prediction improvement. The simulation uses regenerated initial conditions.

04 / Study Table 43

FHN physical-factor accessibility — B. β

Sources 42/43/44; ID, OOD-Intra and OOD-Extra kept separate

Training-fitted K1 factor probe R² ↑

FHN physical-factor accessibility — B. β
Split	Method	Src 42	Src 43	Src 44
ID	NOD	0.9627	0.9496	0.9394
ID	SPRII	0.9766	0.9449	0.9097
Intra	NOD	0.9877	0.9829	0.9765
Intra	SPRII	0.9600	0.9269	0.8990
Extra	NOD	0.9521	0.9409	0.9299
Extra	SPRII	0.9848	0.9518	0.9154

Bold marks the higher β-probe R² within each matched split × source comparison.

Dashed rules separate evaluation splits.

ID · NODThe favorable method changes with split and source. Bold is a descriptive ordering, not a significance mark.

Training-fitted K1 probes measure β accessibility separately by source and split. The favorable method varies across these matched comparisons; probe orderings are not a prediction or fixed-use result. The simulation uses regenerated initial conditions.