Atomizer/studies/m1_mirror_adaptive_V11

M1 Mirror Adaptive Surrogate Optimization V11

Adaptive neural surrogate optimization with real FEA validation for the M1 telescope mirror support system.

Created: 2025-12-03 Protocol: Adaptive Surrogate (TPE + FEA Validation Loop) Status: Ready to Run

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1. Engineering Problem

1.1 Objective

Minimize gravitational wavefront error (WFE) deformations in a 1.2m telescope primary mirror across operational angles (20-60 deg elevation) and manufacturing orientation (90 deg polishing).

1.2 Physical System

• Component: M1 Primary Mirror Assembly with whiffle-tree support
• Material: Zerodur glass ceramic (E=91 GPa, CTE~0)
• Loading: Self-weight gravity at multiple elevation angles
• Boundary Conditions: 18-point whiffle-tree axial support, 3-point lateral support
• Analysis Type: Linear static (Nastran SOL 101) with 4 subcases (20, 40, 60, 90 deg)

1.3 Optical Workflow

Reference: 20 deg (interferometer baseline)

Operational Tracking:
  - 40 deg - 20 deg = tracking deformation at 40 deg
  - 60 deg - 20 deg = tracking deformation at 60 deg

Manufacturing:
  - 90 deg - 20 deg = polishing correction needed

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2. Mathematical Formulation

2.1 Objectives

Objective	Goal	Weight	Formula	Target	Units
Operational 40-20	minimize	5.0	\text{RMS}_{filt}(Z_{40} - Z_{20})	4.0	nm
Operational 60-20	minimize	5.0	\text{RMS}_{filt}(Z_{60} - Z_{20})	10.0	nm
Manufacturing 90-20	minimize	1.0	\text{RMS}_{J1-J3}(Z_{90} - Z_{20})	20.0	nm

Where:

• Z_\theta = Zernike coefficients at elevation angle \theta
• \text{RMS}_{filt} = RMS with J1-J4 (piston, tip, tilt, defocus) removed
• \text{RMS}_{J1-J3} = RMS with only J1-J3 (piston, tip, tilt) removed

2.2 Design Variables

Parameter	Symbol	Bounds	Units	Description
lateral_inner_angle	\alpha_i	[25.0, 28.5]	deg	Inner lateral support angle
lateral_outer_angle	\alpha_o	[13.0, 17.0]	deg	Outer lateral support angle
lateral_outer_pivot	p_o	[9.0, 12.0]	mm	Outer pivot position
lateral_inner_pivot	p_i	[9.0, 12.0]	mm	Inner pivot position
lateral_middle_pivot	p_m	[18.0, 23.0]	mm	Middle pivot position
lateral_closeness	c_l	[9.5, 12.5]	mm	Lateral support spacing
whiffle_min	w_{min}	[35.0, 55.0]	mm	Whiffle tree minimum
whiffle_outer_to_vertical	w_{ov}	[68.0, 80.0]	deg	Whiffle outer to vertical
whiffle_triangle_closeness	w_{tc}	[50.0, 65.0]	mm	Whiffle triangle spacing
blank_backface_angle	\beta	[3.5, 5.0]	deg	Mirror blank backface angle
inner_circular_rib_dia	d_{rib}	[480.0, 620.0]	mm	Inner rib diameter

Design Space: \mathbf{x} \in \mathbb{R}^{11}

2.3 Weighted Objective

f(\mathbf{x}) = \frac{w_1 \cdot \frac{O_{40-20}}{t_1} + w_2 \cdot \frac{O_{60-20}}{t_2} + w_3 \cdot \frac{O_{mfg}}{t_3}}{w_1 + w_2 + w_3}

Where w_i are weights and t_i are target values for normalization.

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3. Adaptive Optimization Algorithm

3.1 Configuration

Parameter	Value	Description
Algorithm	TPE + FEA Validation	Bayesian optimization with real validation
NN Trials/Iteration	1000	Fast surrogate exploration
FEA Trials/Iteration	5	Real validation per iteration
Strategy	Hybrid	70% best + 30% uncertain (exploration)
Convergence	0.3 nm threshold	Stop if no improvement
Patience	5 iterations	Iterations without improvement before stopping

3.2 Adaptive Loop

┌─────────────────────────────────────────────────────────────────────┐
│                    ADAPTIVE OPTIMIZATION LOOP                        │
├─────────────────────────────────────────────────────────────────────┤
│                                                                      │
│  1. LOAD V10 FEA DATA (90 trials)                                   │
│     └─ Cross-link: ../m1_mirror_zernike_optimization_V10/           │
│                                                                      │
│  2. TRAIN INITIAL SURROGATE                                         │
│     └─ MLP: 11 inputs → 3 objectives                                │
│     └─ Architecture: [128, 256, 256, 128, 64]                       │
│                                                                      │
│  3. ITERATION LOOP:                                                 │
│     │                                                                │
│     ├─ 3a. SURROGATE EXPLORATION (1000 NN trials)                   │
│     │      └─ TPE sampler with MC Dropout uncertainty               │
│     │                                                                │
│     ├─ 3b. CANDIDATE SELECTION                                      │
│     │      └─ Hybrid: best weighted + highest uncertainty           │
│     │                                                                │
│     ├─ 3c. FEA VALIDATION (5 real simulations)                      │
│     │      └─ NX Nastran SOL 101 with ZernikeExtractor              │
│     │      └─ Tag trials: source='FEA'                              │
│     │                                                                │
│     ├─ 3d. UPDATE BEST & CHECK IMPROVEMENT                          │
│     │      └─ Track no_improvement_count                            │
│     │                                                                │
│     ├─ 3e. RETRAIN SURROGATE                                        │
│     │      └─ Include new FEA data                                  │
│     │                                                                │
│     └─ 3f. CONVERGENCE CHECK                                        │
│            └─ Stop if patience exceeded                             │
│                                                                      │
│  4. SAVE FINAL RESULTS                                              │
│     └─ Best FEA-validated design                                    │
│                                                                      │
└─────────────────────────────────────────────────────────────────────┘

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4. Result Extraction Methods

4.1 Relative Filtered RMS Extraction

Attribute	Value
Extractor	ZernikeExtractor.extract_relative()
Module	optimization_engine.extractors.extract_zernike
Source	.op2 file from NX Nastran
Output	nm (nanometers)

Algorithm:

1. Parse OP2 displacement results for target and reference subcases
2. Fit Zernike polynomials (Noll indexing, J1-J50)
3. Compute difference: \Delta Z_j = Z_j^{target} - Z_j^{ref}
4. Filter low orders (J1-J4 for operational, J1-J3 for manufacturing)
5. Compute RMS: \text{RMS} = \sqrt{\sum_{j} \Delta Z_j^2}

Code:

from optimization_engine.extractors import ZernikeExtractor

extractor = ZernikeExtractor(op2_path, displacement_unit='mm', n_modes=50)

# Operational objectives
rel_40 = extractor.extract_relative("3", "2")  # 40 deg vs 20 deg
obj_40_20 = rel_40['relative_filtered_rms_nm']

rel_60 = extractor.extract_relative("4", "2")  # 60 deg vs 20 deg
obj_60_20 = rel_60['relative_filtered_rms_nm']

# Manufacturing objective
rel_90 = extractor.extract_relative("1", "2")  # 90 deg vs 20 deg
obj_mfg = rel_90['relative_rms_filter_j1to3']

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5. Neural Surrogate

5.1 Architecture

Input (11) → Dense(128) → BN → ReLU → Dropout(0.1)
          → Dense(256) → BN → ReLU → Dropout(0.1)
          → Dense(256) → BN → ReLU → Dropout(0.1)
          → Dense(128) → BN → ReLU → Dropout(0.1)
          → Dense(64)  → BN → ReLU → Dropout(0.1)
          → Dense(3) → Output

5.2 MC Dropout Uncertainty

For candidate selection, MC Dropout provides uncertainty estimates:

• Enable dropout at inference time
• Run 30 forward passes
• Compute mean and std of predictions
• High std = high uncertainty = exploration candidate

5.3 Training Configuration

Setting	Value
Optimizer	AdamW
Learning Rate	0.001
Weight Decay	1e-4
Scheduler	CosineAnnealing
Epochs	300
Batch Size	16

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6. Study File Structure

m1_mirror_adaptive_V11/
│
├── 1_setup/                              # INPUT CONFIGURATION
│   ├── model/                            # NX Model Files (copied from V10)
│   │   └── [NX files copied on first run]
│   └── optimization_config.json          # Study configuration
│
├── 2_iterations/                         # FEA iteration folders
│   └── iter{N}/                          # Per-trial working directory
│
├── 3_results/                            # OUTPUT
│   ├── study.db                          # Optuna database (NN trials)
│   ├── adaptive_state.json               # Iteration state
│   ├── surrogate_*.pt                    # Model checkpoints
│   ├── final_results.json                # Best results
│   └── optimization.log                  # Execution log
│
├── run_optimization.py                   # Main entry point
├── README.md                             # This blueprint
└── STUDY_REPORT.md                       # Results report (updated as runs)

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7. Dashboard Integration

Trial Source Differentiation

Source	Tag	Display
V10 FEA	V10_FEA	Used for training only
V11 FEA	FEA	Blue circles
V11 NN	NN	Orange crosses

Attributes Stored

For each trial:

• source: 'FEA' or 'NN'
• predicted_40_vs_20: NN prediction (if NN)
• predicted_60_vs_20: NN prediction (if NN)
• predicted_mfg: NN prediction (if NN)

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8. Quick Start

# Navigate to study
cd studies/m1_mirror_adaptive_V11

# Start adaptive optimization
python run_optimization.py --start

# With custom settings
python run_optimization.py --start --fea-batch 3 --patience 7

# Monitor in dashboard
# FEA trials: Blue circles
# NN trials: Orange crosses

Command Line Options

Option	Default	Description
--start	-	Required to begin optimization
--fea-batch	5	FEA validations per iteration
--nn-trials	1000	NN trials per iteration
--patience	5	Iterations without improvement
--strategy	hybrid	best / uncertain / hybrid

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9. Configuration Reference

File: 1_setup/optimization_config.json

Section	Key	Description
source_study.database	../m1_mirror_zernike_optimization_V10/3_results/study.db	V10 training data
objectives[]	3 objectives	Relative filtered RMS metrics
adaptive_settings.*	Iteration config	NN trials, FEA batch, patience
surrogate_settings.*	Neural config	Architecture, dropout, MC samples
dashboard_settings.*	Visualization	FEA/NN markers and colors

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10. References

• Deb et al. (2002). A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evolutionary Computation.
• Noll, R.J. (1976). Zernike polynomials and atmospheric turbulence. JOSA.
• Gal, Y. & Ghahramani, Z. (2016). Dropout as a Bayesian Approximation. ICML.
• Optuna Documentation: Tree-structured Parzen Estimator (TPE) sampler.

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Generated by Atomizer Framework. Study cross-links V10 FEA data for surrogate training.