DynamisLab/src/OID_analysis/Final_Conclusions.md

OID Analysis: Final Conclusions

(Phase 2 completed 2026-06-15)

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Six Questions Answered

Q1: Steady cloak -- which correction structures determine suppression/restoration?

Answer: The force-OID and suppression-OID mode 1 overlap at 0.763, indicating that force-generating and fluctuation-suppressing correction structures are highly related but not identical. The steady cloak achieves 99.43% full-field RMS reduction and 38.5% recirculation area collapse. The dominant correction structures are concentrated in the near-body zone and strongly project onto total force (cum_corr=0.88 in one mode). The recirculation length barely changes (3.2% collapse) while area drops 38.5%, suggesting the control narrows the wake bubble without fully eliminating it.

• POD rank: r=10 (99.97% energy in 5 modes). Rank sensitivity: 1.000.
• Metric: RMS reduction, Lr/Ar collapse (NOT time-series R2).

Q2: Karman cloak -- which correction structures determine incoming-street preservation?

Answer: Force-OID (S=[0.966, 0.724]) distributes force correlation across two modes (cum_corr 0.572, 1.0). The signature-OID for delayed sensor error performs similarly to current error (cum_corr 0.967 vs 0.965), suggesting the correction structures respond synchronously with the incoming street rather than predicting it ahead of time. The OID coordinate for force prediction achieves R2=0.750 (vs POD's 0.418), a clear OID advantage. However, OID-only captures only 22.5% of action variance (vs obs->act at 95.6%), meaning OID coordinates identify force-relevant structures but do NOT capture the full control law.

• Delay: tau_c=25 steps. POD rank: r=10. Rank sensitivity: 1.000.
• Status: Preliminary. Future signature prediction failed (R2~0) due to near-zero variance in the delayed error observable at the chosen delay.

Q3: Illusion -- which correction structures determine target-shedding retuning?

Answer: Signature-OID significantly outperforms POD for signature prediction across all diameters. The strongest effect is at 0.75L (Sig-OID R2=0.661 vs POD -0.034). Performance degrades at larger diameters (1.5L: Sig-OID R2=0.315 vs POD 0.060). Force-OID also strongly outperforms POD for force prediction. The signature-PCD (whitened) does NOT outperform simple signature-OID, suggesting the multi-time-window whitening may be overkill for the current data quality.

• POD rank: r=10. Rank sensitivity: 1.000.
• Delay: tau_c varies by SI (0.75L:~50, 1.0L:~33, 1.5L:~25 steps).

Q4: Force-relevant vs signature-relevant structures -- same or different?

Answer: Systematically different, and their separation increases with task complexity.

Scene	Cosine similarity	Temperature
steady_cloak	+0.763	Force and suppression are highly related
karman_re100	-0.034	Nearly orthogonal
illusion_0.75L	-0.082	Near-orthogonal
illusion_1.0L	-0.495	Moderate divergence
illusion_1.5L	-0.932	Strong divergence

This monotonic pattern from positive (steady) through zero (Karman) to increasingly negative (illusion with growing diameter) is the most striking result of this analysis. It suggests:

• Steady cloak: suppressing force IS the suppression mechanism (same structures).
• Karman cloak: preserving a vortex street requires correction structures that are orthogonal to force generation.
• Illusion: retuning to a different shedding frequency requires correction structures that increasingly oppose the natural force-generating modes as the target mismatch grows.

This directly supports the task-book hypothesis that force-OID and signature-OID must be reported separately, and their divergence is a mechanism result, not a failure.

Q5: Scene commonality -- shared structures?

Answer: The cross-scene mode overlap analysis (from the master table) shows that force-OID and signature-OID modes behave systematically across scenes, but with different quantitative relationships per scene. The common pattern is that correction-field POD captures 98-99.9% energy in 5 modes for ALL scenes -- meaning the correction structures are consistently low-dimensional. However, which correction structures are task-relevant shifts systematically from suppression (steady) to preservation (Karman) to retuning (illusion).

Q6: Is OID better than POD?

Answer: Yes, for all scenes where comparison is meaningful.

Scene	Task	OID R2 (m=2)	POD R2 (m=2)	OID wins?
karman	Force prediction	0.750	0.418	YES
illusion_0.75L	Force prediction	0.435	-2.426	YES
illusion_0.75L	Sig prediction	0.661	-0.034	YES
illusion_1.0L	Force prediction	0.671	-0.237	YES
illusion_1.0L	Sig prediction	0.586	-0.160	YES
illusion_1.5L	Force prediction	0.640	0.264	YES
illusion_1.5L	Sig prediction	0.315	0.060	YES

OID consistently provides positive R2 where POD gives negative or near-zero values. The success criterion from the task book ("OID/PCD with m<=3 beats POD with m<=3") is satisfied for all scenes.

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Additional Conclusions

Control law completeness

The white-box analysis shows that OID coordinates alone capture only 22.5% of the Karman control law (vs 95.6% for raw sensor observations). This is expected and appropriate: OID identifies correction structures most relevant to force/signature, but the PPO policy uses additional information (e.g., FIFO state, target history) beyond what is captured by the correction-field POD subspace.

Illusion q_blk importance

The requirement to separately collect illusion-position q_blk was validated: the geometry differences (front_x 19 vs 30, sensor_x 30 vs 40) would have contaminated Delta_q_ctl with position mismatches. Using the cloak-position q_blk would have produced a Delta_q_ctl dominated not by control effects but by geometric displacement -- invalidating all subsequent OID analysis.

Future work recommendations

1. Investigate the Karman future-sig R2~0 result: The delayed sensor error observable may need a different delay or a different formulation (e.g., phase-error instead of direct error).
2. Connect OID coordinates to SINDy white-box framework: The OID coordinates could be input features for SINDy, potentially giving a lower-dimensional control law.
3. Phase-conditioned analysis for periodic cases: Instead of delay-embedded OID, try phase-conditioned OID where each phase of the shedding cycle is analyzed separately.
4. Check rank sensitivity for the force-vs-sig overlap divergence: The systematic trend from +0.763 to -0.932 is compelling but needs verification across multiple POD ranks.