# M1 Mirror Pure NSGA-II FEA Optimization V13

Pure multi-objective FEA optimization with NSGA-II sampler for the M1 telescope mirror support system.

**Created**: 2025-12-09
**Protocol**: Pure NSGA-II Multi-Objective (No Neural Surrogate)
**Status**: Running

---

## 1. Purpose

V13 runs **pure FEA optimization** without any neural surrogate to establish ground-truth Pareto front. This serves as:

1. **Baseline** for evaluating GNN/MLP surrogate accuracy
2. **Ground truth** Pareto front for comparison
3. **Validation data** for future surrogate training

### Key Difference from V11/V12

| Aspect | V11 (Adaptive MLP) | V12 (GNN + Validation) | V13 (Pure FEA) |
|--------|-------------------|------------------------|----------------|
| Surrogate | MLP (4-layer) | Zernike GNN | None |
| Sampler | TPE | NSGA-II | NSGA-II |
| Trials/hour | ~100 NN + 5 FEA | ~5000 GNN + 5 FEA | 6-7 FEA |
| Purpose | Fast exploration | Field prediction | Ground truth |

---

## 2. Seeding Strategy

V13 seeds from **all prior FEA data** in V11 and V12:

```
V11 (107 FEA trials) + V12 (131 FEA trials) = 238 total
                                               │
                                    ┌──────────┴──────────┐
                                    │  Parameter Filter   │
                                    │  (blank_backface    │
                                    │   4.0-5.0 range)    │
                                    └──────────┬──────────┘
                                               │
                                    217 trials seeded into V13
```

### Why 21 Trials Were Skipped

V13 config uses `blank_backface_angle: [4.0, 5.0]` (intentionally narrower).
Trials from V10/V11 with `blank_backface_angle < 4.0` (range was 3.5-5.0) were rejected by Optuna.

---

## 3. Mathematical Formulation

### 3.1 Objectives (Same as V11/V12)

| Objective | Goal | Formula | Target | Units |
|-----------|------|---------|--------|-------|
| `rel_filtered_rms_40_vs_20` | minimize | RMS_filt(Z_40 - Z_20) | 4.0 | nm |
| `rel_filtered_rms_60_vs_20` | minimize | RMS_filt(Z_60 - Z_20) | 10.0 | nm |
| `mfg_90_optician_workload` | minimize | RMS_J1-J3(Z_90 - Z_20) | 20.0 | nm |

### 3.2 Design Variables (11)

| Parameter | Bounds | Units |
|-----------|--------|-------|
| lateral_inner_angle | [25.0, 28.5] | deg |
| lateral_outer_angle | [13.0, 17.0] | deg |
| lateral_outer_pivot | [9.0, 12.0] | mm |
| lateral_inner_pivot | [9.0, 12.0] | mm |
| lateral_middle_pivot | [18.0, 23.0] | mm |
| lateral_closeness | [9.5, 12.5] | mm |
| whiffle_min | [35.0, 55.0] | mm |
| whiffle_outer_to_vertical | [68.0, 80.0] | deg |
| whiffle_triangle_closeness | [50.0, 65.0] | mm |
| blank_backface_angle | [4.0, 5.0] | deg |
| inner_circular_rib_dia | [480.0, 620.0] | mm |

---

## 4. NSGA-II Configuration

```python
sampler = NSGAIISampler(
    population_size=50,
    crossover=SBXCrossover(eta=15),
    mutation=PolynomialMutation(eta=20),
    seed=42
)
```

NSGA-II performs true multi-objective optimization:
- **Non-dominated sorting** for Pareto ranking
- **Crowding distance** for diversity preservation
- **No scalarization** - preserves full Pareto front

---

## 5. Study Structure

```
m1_mirror_adaptive_V13/
├── 1_setup/
│   ├── model/                    # NX model files (from V11)
│   └── optimization_config.json  # Study config
├── 2_iterations/
│   └── iter{N}/                  # FEA working directories
│       ├── *.prt, *.fem, *.sim   # NX files
│       ├── params.exp            # Parameter expressions
│       └── *solution_1.op2       # Results
├── 3_results/
│   └── study.db                  # Optuna database
├── run_optimization.py           # Main entry point
└── README.md                     # This file
```

---

## 6. Usage

```bash
# Start fresh optimization
python run_optimization.py --start --trials 55

# Resume after interruption (Windows update, etc.)
python run_optimization.py --start --trials 35 --resume

# Check status
python run_optimization.py --status
```

### Expected Runtime

- ~8-10 min per FEA trial
- 55 trials ≈ 7-8 hours overnight

---

## 7. Trial Sources in Database

| Source Tag | Count | Description |
|------------|-------|-------------|
| `V11_FEA` | 5 | V11-only FEA trials |
| `V11_V10_FEA` | 81 | V11 trials inherited from V10 |
| `V12_FEA` | 41 | V12-only FEA trials |
| `V12_V10_FEA` | 90 | V12 trials inherited from V10 |
| `FEA` | 10+ | New V13 FEA trials |

Query trial sources:
```sql
SELECT value_json, COUNT(*)
FROM trial_user_attributes
WHERE key = 'source'
GROUP BY value_json;
```

---

## 8. Post-Processing

### Extract Pareto Front

```python
import optuna

study = optuna.load_study(
    study_name="m1_mirror_V13_nsga2",
    storage="sqlite:///3_results/study.db"
)

# Get Pareto-optimal trials
pareto = study.best_trials

# Print Pareto front
for t in pareto:
    print(f"Trial {t.number}: {t.values}")
```

### Compare to GNN Predictions

```python
# Load V13 FEA Pareto front
# Load GNN predictions from V12
# Compute error: |GNN - FEA| / FEA
```

---

## 9. Results (To Be Updated)

| Metric | Value |
|--------|-------|
| Seeded trials | 217 |
| New FEA trials | TBD |
| Pareto front size | TBD |
| Best rel_rms_40 | TBD |
| Best rel_rms_60 | TBD |
| Best mfg_90 | TBD |

---

## 10. Cross-References

- **V10**: `../m1_mirror_zernike_optimization_V10/` - Original LHS sampling
- **V11**: `../m1_mirror_adaptive_V11/` - MLP adaptive surrogate
- **V12**: `../m1_mirror_adaptive_V12/` - GNN field prediction

---

*Generated by Atomizer Framework. Pure NSGA-II for ground-truth Pareto optimization.*