# 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 2*NX*NY 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