# M1 Mirror Adaptive Surrogate Optimization V12

Adaptive neural-accelerated optimization of telescope primary mirror (M1) support structure using Zernike wavefront error decomposition with **auto-tuned hyperparameters**, **ensemble surrogates**, and **mass constraints**.

**Created**: 2024-12-04
**Protocol**: Protocol 12 (Adaptive Hybrid FEA/Neural with Hyperparameter Tuning)
**Status**: Running
**Source Data**: V11 (107 FEA samples)

---

## 1. Engineering Problem

### 1.1 Objective

Optimize the telescope primary mirror (M1) whiffle tree and lateral support structure to minimize wavefront error (WFE) across different gravity orientations while maintaining mass under 99 kg.

### 1.2 Physical System

| Property | Value |
|----------|-------|
| **Component** | M1 primary mirror assembly with whiffle tree support |
| **Material** | Borosilicate glass (mirror blank), steel (support structure) |
| **Loading** | Gravity at multiple zenith angles (90°, 20°, 40°, 60°) |
| **Boundary Conditions** | Whiffle tree kinematic mount with lateral supports |
| **Analysis Type** | Linear static multi-subcase (Nastran SOL 101) |
| **Subcases** | 4 orientations with different gravity vectors |
| **Output** | Surface deformation → Zernike polynomial decomposition |

### 1.3 Key Improvements in V12

| Feature | V11 | V12 |
|---------|-----|-----|
| Hyperparameter Tuning | Fixed architecture | Optuna auto-tuning |
| Model Architecture | Single network | Ensemble of 3 models |
| Validation | Train/test split | K-fold cross-validation |
| Mass Constraint | Post-hoc check | Integrated penalty |
| Convergence | Fixed iterations | Early stopping with patience |

---

## 2. Mathematical Formulation

### 2.1 Objectives

| Objective | Goal | Weight | Formula | Units | Target |
|-----------|------|--------|---------|-------|--------|
| `rel_filtered_rms_40_vs_20` | minimize | 5.0 | $\sigma_{40/20} = \sqrt{\sum_{j=5}^{50} (Z_j^{40} - Z_j^{20})^2}$ | nm | 4 nm |
| `rel_filtered_rms_60_vs_20` | minimize | 5.0 | $\sigma_{60/20} = \sqrt{\sum_{j=5}^{50} (Z_j^{60} - Z_j^{20})^2}$ | nm | 10 nm |
| `mfg_90_optician_workload` | minimize | 1.0 | $\sigma_{90}^{J4+} = \sqrt{\sum_{j=4}^{50} (Z_j^{90} - Z_j^{20})^2}$ | nm | 20 nm |

**Weighted Sum Objective**:
$$J(\mathbf{x}) = \sum_{i=1}^{3} w_i \cdot \frac{f_i(\mathbf{x})}{t_i} + P_{mass}(\mathbf{x})$$

Where:
- $w_i$ = weight for objective $i$
- $f_i(\mathbf{x})$ = objective value
- $t_i$ = target value (normalization)
- $P_{mass}$ = mass constraint penalty

### 2.2 Zernike Decomposition

The wavefront error $W(r,\theta)$ is decomposed into Noll-indexed Zernike polynomials:

$$W(r,\theta) = \sum_{j=1}^{50} Z_j \cdot P_j(r,\theta)$$

**WFE from Displacement** (reflection factor of 2):
$$W_{nm} = 2 \cdot \delta_z \cdot 10^6$$

Where $\delta_z$ is the Z-displacement in mm.

**Filtered RMS** (excluding alignable terms J1-J4):
$$\sigma_{filtered} = \sqrt{\sum_{j=5}^{50} Z_j^2}$$

**Manufacturing RMS** (excluding J1-J3, keeping defocus J4):
$$\sigma_{mfg} = \sqrt{\sum_{j=4}^{50} Z_j^2}$$

### 2.3 Design Variables (11 Parameters)

| Parameter | Symbol | Bounds | Baseline | Units | Description |
|-----------|--------|--------|----------|-------|-------------|
| `lateral_inner_angle` | $\alpha_{in}$ | [25, 28.5] | 26.79 | deg | Inner lateral support angle |
| `lateral_outer_angle` | $\alpha_{out}$ | [13, 17] | 14.64 | deg | Outer lateral support angle |
| `lateral_outer_pivot` | $p_{out}$ | [9, 12] | 10.40 | mm | Outer pivot offset |
| `lateral_inner_pivot` | $p_{in}$ | [9, 12] | 10.07 | mm | Inner pivot offset |
| `lateral_middle_pivot` | $p_{mid}$ | [18, 23] | 20.73 | mm | Middle pivot offset |
| `lateral_closeness` | $c_{lat}$ | [9.5, 12.5] | 11.02 | mm | Lateral support spacing |
| `whiffle_min` | $w_{min}$ | [35, 55] | 40.55 | mm | Whiffle tree minimum |
| `whiffle_outer_to_vertical` | $\theta_w$ | [68, 80] | 75.67 | deg | Outer whiffle angle |
| `whiffle_triangle_closeness` | $c_w$ | [50, 65] | 60.00 | mm | Whiffle triangle spacing |
| `blank_backface_angle` | $\beta$ | [4.0, 5.0] | 4.23 | deg | Mirror backface angle (mass driver) |
| `inner_circular_rib_dia` | $D_{rib}$ | [480, 620] | 534.00 | mm | Inner rib diameter |

**Design Space**:
$$\mathbf{x} = [\alpha_{in}, \alpha_{out}, p_{out}, p_{in}, p_{mid}, c_{lat}, w_{min}, \theta_w, c_w, \beta, D_{rib}]^T \in \mathbb{R}^{11}$$

### 2.4 Mass Constraint

| Constraint | Type | Formula | Threshold | Handling |
|------------|------|---------|-----------|----------|
| `mass_limit` | upper_bound | $m(\mathbf{x}) \leq m_{max}$ | 99 kg | Penalty in objective |

**Penalty Function**:
$$P_{mass}(\mathbf{x}) = \begin{cases}
0 & \text{if } m \leq 99 \\
100 \cdot (m - 99) & \text{if } m > 99
\end{cases}$$

**Mass Estimation** (from `blank_backface_angle`):
$$\hat{m}(\beta) = 105 - 15 \cdot (\beta - 4.0) \text{ kg}$$

---

## 3. Optimization Algorithm

### 3.1 Adaptive Hybrid Strategy

| Parameter | Value | Description |
|-----------|-------|-------------|
| Algorithm | Adaptive Hybrid | FEA + Neural Surrogate |
| Surrogate | Tuned Ensemble (3 models) | Auto-tuned architecture |
| Sampler | TPE | Tree-structured Parzen Estimator |
| Max Iterations | 100 | Adaptive loop iterations |
| FEA Batch Size | 5 | Real FEA evaluations per iteration |
| NN Trials | 1000 | Surrogate evaluations per iteration |
| Patience | 5 | Early stopping threshold |
| Convergence | 0.3 nm | Objective improvement threshold |

### 3.2 Hyperparameter Tuning

| Setting | Value |
|---------|-------|
| Tuning Trials | 30 |
| Cross-Validation | 5-fold |
| Search Space | Hidden dims, dropout, learning rate |
| Ensemble Size | 3 models |
| MC Dropout Samples | 30 |

**Tuned Architecture**:
```
Input(11) → Linear(128) → ReLU → Dropout →
Linear(256) → ReLU → Dropout →
Linear(256) → ReLU → Dropout →
Linear(128) → ReLU → Dropout →
Linear(64) → ReLU → Linear(4)
```

### 3.3 Adaptive Loop Flow

```
┌─────────────────────────────────────────────────────────────────────────┐
│                      ADAPTIVE ITERATION k                                │
├─────────────────────────────────────────────────────────────────────────┤
│                                                                          │
│  1. SURROGATE EXPLORATION (1000 trials)                                 │
│     ├── Sample 11 design variables via TPE                              │
│     ├── Predict objectives with ensemble (mean + uncertainty)           │
│     └── Select top candidates (exploitation) + diverse (exploration)    │
│                                                                          │
│  2. FEA VALIDATION (5 trials)                                           │
│     ├── Run NX Nastran SOL 101 (4 subcases)                             │
│     ├── Extract Zernike coefficients from OP2                           │
│     ├── Compute relative filtered RMS                                    │
│     └── Store in Optuna database                                        │
│                                                                          │
│  3. SURROGATE RETRAINING                                                │
│     ├── Load all FEA data from database                                 │
│     ├── Retrain ensemble with new data                                  │
│     └── Update uncertainty estimates                                    │
│                                                                          │
│  4. CONVERGENCE CHECK                                                   │
│     ├── Δbest < 0.3 nm for patience=5 iterations?                       │
│     └── If converged → STOP, else → next iteration                      │
│                                                                          │
└─────────────────────────────────────────────────────────────────────────┘
```

---

## 4. Simulation Pipeline

### 4.1 FEA Trial Execution Flow

```
┌─────────────────────────────────────────────────────────────────────────┐
│                         FEA TRIAL n EXECUTION                            │
├─────────────────────────────────────────────────────────────────────────┤
│                                                                          │
│  1. CANDIDATE SELECTION                                                 │
│     Hybrid strategy: 70% exploitation (best NN predictions)             │
│                      30% exploration (uncertain regions)                │
│                                                                          │
│  2. NX PARAMETER UPDATE                                                 │
│     Module: optimization_engine/nx_solver.py                            │
│     Target Part: M1_Blank.prt (and related components)                  │
│     Action: Update 11 expressions with new design values                │
│                                                                          │
│  3. NX SIMULATION (Nastran SOL 101 - 4 Subcases)                        │
│     Module: optimization_engine/solve_simulation.py                     │
│     Input: ASSY_M1_assyfem1_sim1.sim                                    │
│     Subcases:                                                           │
│       1 = 90° zenith (polishing/manufacturing)                          │
│       2 = 20° zenith (reference)                                        │
│       3 = 40° zenith (operational target 1)                             │
│       4 = 60° zenith (operational target 2)                             │
│     Output: .dat, .op2, .f06                                            │
│                                                                          │
│  4. ZERNIKE EXTRACTION                                                  │
│     Module: optimization_engine/extractors/extract_zernike.py           │
│     a. Read node coordinates from BDF/DAT                               │
│     b. Read Z-displacements from OP2 for each subcase                   │
│     c. Compute RELATIVE displacement (target - reference)               │
│     d. Convert to WFE: W = 2 × Δδz × 10⁶ nm                             │
│     e. Fit 50 Zernike coefficients via least-squares                    │
│     f. Compute filtered RMS (exclude J1-J4)                             │
│                                                                          │
│  5. MASS EXTRACTION                                                     │
│     Module: optimization_engine/extractors/extract_mass_from_expression │
│     Expression: p173 (CAD mass property)                                │
│                                                                          │
│  6. OBJECTIVE COMPUTATION                                               │
│     rel_filtered_rms_40_vs_20 ← Zernike RMS (subcase 3 - 2)            │
│     rel_filtered_rms_60_vs_20 ← Zernike RMS (subcase 4 - 2)            │
│     mfg_90_optician_workload ← Zernike RMS J4+ (subcase 1 - 2)         │
│                                                                          │
│  7. WEIGHTED OBJECTIVE + MASS PENALTY                                   │
│     J = Σ (weight × objective / target) + mass_penalty                  │
│                                                                          │
│  8. STORE IN DATABASE                                                   │
│     Optuna SQLite: 3_results/study.db                                   │
│     User attrs: trial_source='fea', mass_kg, all Zernike coefficients   │
│                                                                          │
└─────────────────────────────────────────────────────────────────────────┘
```

### 4.2 Subcase Configuration

| Subcase | Zenith Angle | Gravity Direction | Role |
|---------|--------------|-------------------|------|
| 1 | 90° | Horizontal | Manufacturing/polishing reference |
| 2 | 20° | Near-vertical | Operational reference (baseline) |
| 3 | 40° | Mid-elevation | Operational target 1 |
| 4 | 60° | Low-elevation | Operational target 2 |

---

## 5. Result Extraction Methods

### 5.1 Zernike WFE Extraction

| Attribute | Value |
|-----------|-------|
| **Extractor** | `ZernikeExtractor` |
| **Module** | `optimization_engine.extractors.extract_zernike` |
| **Method** | `extract_relative()` |
| **Geometry Source** | `.dat` (BDF format, auto-detected) |
| **Displacement Source** | `.op2` (OP2 binary) |
| **Output** | 50 Zernike coefficients + RMS metrics per subcase pair |

**Algorithm**:

1. Load node coordinates $(X_i, Y_i)$ from BDF
2. Load Z-displacements $\delta_{z,i}$ from OP2 for each subcase
3. Compute relative displacement (node-by-node):
   $$\Delta\delta_{z,i} = \delta_{z,i}^{target} - \delta_{z,i}^{reference}$$
4. Convert to WFE:
   $$W_i = 2 \cdot \Delta\delta_{z,i} \cdot 10^6 \text{ nm}$$
5. Fit Zernike coefficients via least-squares:
   $$\min_{\mathbf{Z}} \| \mathbf{W} - \mathbf{P} \mathbf{Z} \|^2$$
6. Compute filtered RMS:
   $$\sigma_{filtered} = \sqrt{\sum_{j=5}^{50} Z_j^2}$$

**Code**:
```python
from optimization_engine.extractors import ZernikeExtractor

extractor = ZernikeExtractor(op2_file, bdf_file)
result = extractor.extract_relative(
    target_subcase="3",      # 40 deg
    reference_subcase="2",   # 20 deg
    displacement_unit="mm"
)
filtered_rms = result['relative_filtered_rms_nm']  # nm
```

### 5.2 Mass Extraction

| Attribute | Value |
|-----------|-------|
| **Extractor** | `extract_mass_from_expression` |
| **Module** | `optimization_engine.extractors` |
| **Expression** | `p173` (CAD mass property) |
| **Output** | kg |

**Code**:
```python
from optimization_engine.extractors import extract_mass_from_expression

mass_kg = extract_mass_from_expression(model_file, expression_name="p173")
```

---

## 6. Neural Acceleration (Tuned Ensemble Surrogate)

### 6.1 Configuration

| Setting | Value | Description |
|---------|-------|-------------|
| `enabled` | `true` | Neural surrogate active |
| `model_type` | `TunedEnsembleSurrogate` | Ensemble of tuned networks |
| `ensemble_size` | 3 | Number of models in ensemble |
| `hidden_dims` | `[128, 256, 256, 128, 64]` | Auto-tuned architecture |
| `dropout` | 0.1 | Regularization |
| `learning_rate` | 0.001 | Adam optimizer |
| `batch_size` | 16 | Mini-batch size |
| `mc_dropout_samples` | 30 | Monte Carlo uncertainty |

### 6.2 Hyperparameter Tuning

| Parameter | Search Space |
|-----------|--------------|
| `n_layers` | [3, 4, 5, 6] |
| `hidden_dim` | [64, 128, 256, 512] |
| `dropout` | [0.0, 0.1, 0.2, 0.3] |
| `learning_rate` | [1e-4, 1e-3, 1e-2] |
| `batch_size` | [8, 16, 32, 64] |

**Tuning Objective**:
$$\mathcal{L}_{tune} = \frac{1}{K} \sum_{k=1}^{K} MSE_{val}^{(k)}$$

Using 5-fold cross-validation.

### 6.3 Surrogate Model

**Input**: $\mathbf{x} = [11 \text{ design variables}]^T \in \mathbb{R}^{11}$

**Output**: $\hat{\mathbf{y}} = [4 \text{ objectives/constraints}]^T \in \mathbb{R}^{4}$
- `rel_filtered_rms_40_vs_20` (nm)
- `rel_filtered_rms_60_vs_20` (nm)
- `mfg_90_optician_workload` (nm)
- `mass_kg` (kg)

**Ensemble Prediction**:
$$\hat{y} = \frac{1}{M} \sum_{m=1}^{M} f_m(\mathbf{x})$$

**Uncertainty Quantification** (MC Dropout):
$$\sigma_y^2 = \frac{1}{T} \sum_{t=1}^{T} f_{dropout}^{(t)}(\mathbf{x})^2 - \hat{y}^2$$

### 6.4 Training Data Location

```
m1_mirror_adaptive_V12/
├── 2_iterations/
│   ├── iter_001/           # Iteration 1 working files
│   ├── iter_002/
│   └── ...
├── 3_results/
│   ├── study.db            # Optuna database (all trials)
│   ├── optimization.log    # Detailed log
│   ├── surrogate_best.pt   # Best tuned model weights
│   └── tuning_results.json # Hyperparameter tuning history
```

### 6.5 Expected Performance

| Metric | Value |
|--------|-------|
| Source Data | V11: 107 FEA samples |
| FEA time per trial | 10-15 min |
| Neural time per trial | ~5 ms |
| Speedup | ~120,000x |
| Expected R² | > 0.90 (after tuning) |
| Uncertainty Coverage | ~95% (ensemble + MC dropout) |

---

## 7. Study File Structure

```
m1_mirror_adaptive_V12/
│
├── 1_setup/                              # INPUT CONFIGURATION
│   ├── model/ → symlink to V11          # NX Model Files
│   │   ├── ASSY_M1.prt                   # Top-level assembly
│   │   ├── M1_Blank.prt                  # Mirror blank (expressions)
│   │   ├── ASSY_M1_assyfem1.afm          # Assembly FEM
│   │   ├── ASSY_M1_assyfem1_sim1.sim     # Simulation file
│   │   └── *-solution_1.op2              # Results (generated)
│   │
│   └── optimization_config.json          # Study configuration
│
├── 2_iterations/                         # WORKING DIRECTORY
│   ├── iter_001/                         # Iteration 1 model copy
│   ├── iter_002/
│   └── ...
│
├── 3_results/                            # OUTPUT (auto-generated)
│   ├── study.db                          # Optuna SQLite database
│   ├── optimization.log                  # Structured log
│   ├── surrogate_best.pt                 # Trained ensemble weights
│   ├── tuning_results.json               # Hyperparameter tuning
│   └── convergence.json                  # Iteration history
│
├── run_optimization.py                   # Main entry point
├── final_validation.py                   # FEA validation of best NN trials
├── README.md                             # This blueprint
└── STUDY_REPORT.md                       # Results report (updated during run)
```

---

## 8. Results Location

After optimization, results are stored in `3_results/`:

| File | Description | Format |
|------|-------------|--------|
| `study.db` | Optuna database with all trials (FEA + NN) | SQLite |
| `optimization.log` | Detailed execution log | Text |
| `surrogate_best.pt` | Tuned ensemble model weights | PyTorch |
| `tuning_results.json` | Hyperparameter search history | JSON |
| `convergence.json` | Best value per iteration | JSON |

### 8.1 Trial Identification

Trials are tagged with source:
- **FEA trials**: `trial.user_attrs['trial_source'] = 'fea'`
- **NN trials**: `trial.user_attrs['trial_source'] = 'nn'`

**Dashboard Visualization**:
- FEA trials: Blue circles
- NN trials: Orange crosses

### 8.2 Results Report

See [STUDY_REPORT.md](STUDY_REPORT.md) for:
- Optimization progress and convergence
- Best designs found (FEA-validated)
- Surrogate model accuracy (R², MAE)
- Pareto trade-off analysis
- Engineering recommendations

---

## 9. Quick Start

### Launch Optimization

```bash
cd studies/m1_mirror_adaptive_V12

# Start with default settings (uses V11 FEA data)
python run_optimization.py --start

# Custom tuning parameters
python run_optimization.py --start --tune-trials 30 --ensemble-size 3 --fea-batch 5 --patience 5

# Tune hyperparameters only (no FEA)
python run_optimization.py --tune-only
```

### Command Line Options

| Option | Default | Description |
|--------|---------|-------------|
| `--start` | - | Start adaptive optimization |
| `--tune-only` | - | Only tune hyperparameters, no optimization |
| `--tune-trials` | 30 | Number of hyperparameter tuning trials |
| `--ensemble-size` | 3 | Number of models in ensemble |
| `--fea-batch` | 5 | FEA evaluations per iteration |
| `--patience` | 5 | Early stopping patience |

### Monitor Progress

```bash
# View log
tail -f 3_results/optimization.log

# Check database
sqlite3 3_results/study.db "SELECT COUNT(*) FROM trials WHERE state='COMPLETE'"

# Launch Optuna dashboard
optuna-dashboard sqlite:///3_results/study.db --port 8081
```

### Dashboard Access

| Dashboard | URL | Purpose |
|-----------|-----|---------|
| **Atomizer Dashboard** | http://localhost:3000 | Real-time monitoring |
| **Optuna Dashboard** | http://localhost:8081 | Trial history |

---

## 10. Configuration Reference

**File**: `1_setup/optimization_config.json`

| Section | Key | Description |
|---------|-----|-------------|
| `design_variables[]` | 11 parameters | All lateral/whiffle/blank params |
| `objectives[]` | 3 WFE metrics | Relative filtered RMS |
| `constraints[]` | mass_limit | Upper bound 99 kg |
| `zernike_settings.n_modes` | 50 | Zernike polynomial count |
| `zernike_settings.filter_low_orders` | 4 | Exclude J1-J4 |
| `zernike_settings.subcases` | [1,2,3,4] | Zenith angles |
| `adaptive_settings.max_iterations` | 100 | Loop limit |
| `adaptive_settings.surrogate_trials_per_iter` | 1000 | NN trials |
| `adaptive_settings.fea_batch_size` | 5 | FEA per iteration |
| `adaptive_settings.patience` | 5 | Early stopping |
| `surrogate_settings.ensemble_size` | 3 | Model ensemble |
| `surrogate_settings.mc_dropout_samples` | 30 | Uncertainty samples |

---

## 11. References

- **Deb, K. et al.** (2002). A fast and elitist multiobjective genetic algorithm: NSGA-II. *IEEE TEC*.
- **Noll, R.J.** (1976). Zernike polynomials and atmospheric turbulence. *JOSA*.
- **Wilson, R.N.** (2004). *Reflecting Telescope Optics I*. Springer.
- **Snoek, J. et al.** (2012). Practical Bayesian optimization of machine learning algorithms. *NeurIPS*.
- **Gal, Y. & Ghahramani, Z.** (2016). Dropout as a Bayesian approximation. *ICML*.
- **pyNastran Documentation**: BDF/OP2 parsing for FEA post-processing.
- **Optuna Documentation**: Hyperparameter optimization framework.

---

*Atomizer V12: Where adaptive AI meets precision optics.*