DynamisLab/docs/sr_ccd_oid_mapping.md

SR-CCD-OID Cross-Pipeline Mapping

Purpose

This document maps the three analysis pipelines (SINDy-SR, CCD, OID) onto a unified chain. They are NOT competing approaches — they answer different questions at different positions along the control-to-signature pathway.

Unified Control Analysis Chain

obs --[SR/SINDy]--> act --[CFD/physics]--> dq_ctl --[CCD/OID]--> force/signature
 ^                                                                         |
 |_________________________________________________________________________|
                         closed loop

Link	What happens	Which analysis
obs -> act	DRL policy maps sensor readings to control actions	SR/SINDy (white-box control law extraction)
act -> dq_ctl	Actions modify the flow field; the change relative to uncontrolled baseline is dq_ctl	CFD / data collection
dq_ctl -> force	Which correction structures most project to cylinder forces	CCD (force line), OID
dq_ctl -> signature	Which correction structures most determine future sensor mismatch	CCD (signature line), OID

Pipeline Comparison Table

Aspect	SR / SINDy	CCD	OID / PCD
Primary question	How does the controller map observations to actions?	Which correction structures correlate most with force/action/signature?	What is the unified low-dimensional coordinate that captures observable-related structure?
Input data	Dimensionless obs and actions (time series)	dq_ctl fields (N snapshots x 2NXNY grid) + observable time series (force/action/sensor error)	POD coefficients of dq_ctl + observable time series
Output	Sparse symbolic control law (e.g. a_F = 0.3*sin(u_s1))	CCD mode directions W, modal overlaps O_k, compactness m80, LOCO R2	Low-dimensional coordinate z(t), observable reconstruction error
Key method	STLSQ threshold grid, G-equivariant constraints, SIN activation	POD-reduced CCD (Lyu23-inspired)	Observability Gramian / canonical correlation
Current maturity	Medium — cross-Re shared backbone found, G-equivariance validated	Highest — correction-field framework complete for illusion 0.75L/1.0L/1.5L with force/action/signature lines	Low-medium — framework defined, needs data alignment with CCD
Validation	Leave-one-Re-out cross-validation, closed-loop replay	LOCO (4-fold), blocked split, R2_m80	pending alignment
Key result	Karman cloak cross-Re shared backbone exists (R2 > 0.9 for holdout 200)	1.0L O(dqctl,dqtar)=0.913, m80=1; force/sig separated at tau=0, shared at tau_c	pending

Maturity by Scene

Scene	SR/SINDy	CCD	OID
Karman cloak re50/100/200/400	Existing (cross-Re backbone)	Data ready, analysis deferred	Not started
Illusion 0.75L	Existing	Complete (force/action/sig)	Partial
Illusion 1.0L	Existing	Complete (force/action/sig)	Partial
Illusion 1.5L	Existing	Complete (force/action/sig, special mechanism)	Not started
Steady cloak	Existing	Partial (quantitative metrics done)	Not started
Vortex cloak (lamb/taylor)	Existing	Not started	Not started

How They Assemble Into a Paper Chapter

Chapter Structure Proposal

1. Control Law Extraction (SR/SINDy)

• Question: What is the map from sensor observations to cylinder rotations?
• Deliverable: Symbolic control law for each scene, cross-scene comparison of feature usage
• Evidence: Leave-one-out validation, G-equivariance error < 10%

2. Correction Field Analysis (CCD)

• Question: What flow structures does the controller actually modulate?
• Deliverable:
  • Correction-field decomposition (dq_ctl)
  • Force line: O(dqctl,dqtar) across diameters
  • Action line: compactness m80
  • Signature line: force-sig separation at zero lag, convergence at convective delay
  • 1.5L special mechanism
• Evidence: LOCO validation R2 > 0.4 for all lines

3. Low-Dimensional Coordinate (OID)

• Question: Can we describe controller-relevant structures in a unified low-D coordinate?
• Deliverable: Observable-informed coordinates z for each case, reconstruction error
• Evidence: Reconstruction quality vs POD-baseline

4. Unified Mechanism Discussion

• Synthesize findings from all three analyses
• Key claims to support:
  • Control operates by modifying pinball's existing wake (not generating new flows)
  • Force-relevant correction is low-rank and target-aligned at natural scale
  • Cross-scale illusion uses divergent correction paths
  • Force and signature structures separate at zero lag but converge convectively

Current Gaps by Pipeline

SR/SINDy Gaps

• Illusion cross-diameter comparison not yet unified with CCD's correction-field framework
• Closed-loop validation of extracted control laws needs systematic comparison

CCD Gaps

• Karman cloak analysis deferred (data ready, framework designed)
• Steady cloak needs closed-loop control to be meaningful
• Zone-restricted CCD not yet complete (in progress)

OID Gaps

• Data pipeline not yet aligned with CCD's correction-field format
• No direct comparison of OID coordinates with CCD directions
• Requires full cross-analysis with existing CCD results

Data Compatibility

All three pipelines ultimately read from the same data sources:

• fields_aligned.npz (96 aligned field snapshots)
• controlled.npz / sensors.npz (telemetry)
• configs.py (scene metadata)

The correction-field framework (dq_ctl = q_ctl - q_blk) is the standard analysis object across all three. Any analysis that uses raw q_ctl instead should be explicitly flagged as a cross-check.

Recommendation

For the next phase of work:

1. CCD consolidates current results and adds zone-restricted analysis
2. OID should adopt CCD's data loading (compute_correction_fields.py) and correction-field protocol
3. SR/SINDy should align its cross-diameter comparison with CCD's correction-field O(dqctl,dqtar) results
4. A unifying figure comparing O(dqctl,dqtar) from CCD with SR control-law similarity across diameters would be powerful