Atomizer/studies/M1_Mirror/m1_mirror_adaptive_V12

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)

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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}

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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                      │
│                                                                          │
└─────────────────────────────────────────────────────────────────────────┘

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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:

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:

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 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

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

# 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

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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

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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.

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Atomizer V12: Where adaptive AI meets precision optics.