feat: Add Zernike GNN surrogate module and M1 mirror V12/V13 studies
This commit introduces the GNN-based surrogate for Zernike mirror optimization and the M1 mirror study progression from V12 (GNN validation) to V13 (pure NSGA-II). ## GNN Surrogate Module (optimization_engine/gnn/) New module for Graph Neural Network surrogate prediction of mirror deformations: - `polar_graph.py`: PolarMirrorGraph - fixed 3000-node polar grid structure - `zernike_gnn.py`: ZernikeGNN with design-conditioned message passing - `differentiable_zernike.py`: GPU-accelerated Zernike fitting and objectives - `train_zernike_gnn.py`: ZernikeGNNTrainer with multi-task loss - `gnn_optimizer.py`: ZernikeGNNOptimizer for turbo mode (~900k trials/hour) - `extract_displacement_field.py`: OP2 to HDF5 field extraction - `backfill_field_data.py`: Extract fields from existing FEA trials Key innovation: Design-conditioned convolutions that modulate message passing based on structural design parameters, enabling accurate field prediction. ## M1 Mirror Studies ### V12: GNN Field Prediction + FEA Validation - Zernike GNN trained on V10/V11 FEA data (238 samples) - Turbo mode: 5000 GNN predictions → top candidates → FEA validation - Calibration workflow for GNN-to-FEA error correction - Scripts: run_gnn_turbo.py, validate_gnn_best.py, compute_full_calibration.py ### V13: Pure NSGA-II FEA (Ground Truth) - Seeds 217 FEA trials from V11+V12 - Pure multi-objective NSGA-II without any surrogate - Establishes ground-truth Pareto front for GNN accuracy evaluation - Narrowed blank_backface_angle range to [4.0, 5.0] ## Documentation Updates - SYS_14: Added Zernike GNN section with architecture diagrams - CLAUDE.md: Added GNN module reference and quick start - V13 README: Study documentation with seeding strategy 🤖 Generated with [Claude Code](https://claude.com/claude-code) Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>
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studies/m1_mirror_adaptive_V12/README.md
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# M1 Mirror Adaptive Surrogate Optimization V12
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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**.
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**Created**: 2024-12-04
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**Protocol**: Protocol 12 (Adaptive Hybrid FEA/Neural with Hyperparameter Tuning)
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**Status**: Running
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**Source Data**: V11 (107 FEA samples)
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---
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## 1. Engineering Problem
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### 1.1 Objective
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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.
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### 1.2 Physical System
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| Property | Value |
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|----------|-------|
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| **Component** | M1 primary mirror assembly with whiffle tree support |
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| **Material** | Borosilicate glass (mirror blank), steel (support structure) |
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| **Loading** | Gravity at multiple zenith angles (90°, 20°, 40°, 60°) |
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| **Boundary Conditions** | Whiffle tree kinematic mount with lateral supports |
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| **Analysis Type** | Linear static multi-subcase (Nastran SOL 101) |
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| **Subcases** | 4 orientations with different gravity vectors |
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| **Output** | Surface deformation → Zernike polynomial decomposition |
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### 1.3 Key Improvements in V12
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| Feature | V11 | V12 |
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|---------|-----|-----|
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| Hyperparameter Tuning | Fixed architecture | Optuna auto-tuning |
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| Model Architecture | Single network | Ensemble of 3 models |
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| Validation | Train/test split | K-fold cross-validation |
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| Mass Constraint | Post-hoc check | Integrated penalty |
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| Convergence | Fixed iterations | Early stopping with patience |
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---
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## 2. Mathematical Formulation
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### 2.1 Objectives
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| Objective | Goal | Weight | Formula | Units | Target |
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|-----------|------|--------|---------|-------|--------|
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| `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 |
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| `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 |
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| `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 |
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**Weighted Sum Objective**:
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$$J(\mathbf{x}) = \sum_{i=1}^{3} w_i \cdot \frac{f_i(\mathbf{x})}{t_i} + P_{mass}(\mathbf{x})$$
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Where:
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- $w_i$ = weight for objective $i$
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- $f_i(\mathbf{x})$ = objective value
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- $t_i$ = target value (normalization)
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- $P_{mass}$ = mass constraint penalty
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### 2.2 Zernike Decomposition
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The wavefront error $W(r,\theta)$ is decomposed into Noll-indexed Zernike polynomials:
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$$W(r,\theta) = \sum_{j=1}^{50} Z_j \cdot P_j(r,\theta)$$
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**WFE from Displacement** (reflection factor of 2):
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$$W_{nm} = 2 \cdot \delta_z \cdot 10^6$$
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Where $\delta_z$ is the Z-displacement in mm.
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**Filtered RMS** (excluding alignable terms J1-J4):
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$$\sigma_{filtered} = \sqrt{\sum_{j=5}^{50} Z_j^2}$$
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**Manufacturing RMS** (excluding J1-J3, keeping defocus J4):
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$$\sigma_{mfg} = \sqrt{\sum_{j=4}^{50} Z_j^2}$$
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### 2.3 Design Variables (11 Parameters)
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| Parameter | Symbol | Bounds | Baseline | Units | Description |
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|-----------|--------|--------|----------|-------|-------------|
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| `lateral_inner_angle` | $\alpha_{in}$ | [25, 28.5] | 26.79 | deg | Inner lateral support angle |
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| `lateral_outer_angle` | $\alpha_{out}$ | [13, 17] | 14.64 | deg | Outer lateral support angle |
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| `lateral_outer_pivot` | $p_{out}$ | [9, 12] | 10.40 | mm | Outer pivot offset |
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| `lateral_inner_pivot` | $p_{in}$ | [9, 12] | 10.07 | mm | Inner pivot offset |
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| `lateral_middle_pivot` | $p_{mid}$ | [18, 23] | 20.73 | mm | Middle pivot offset |
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| `lateral_closeness` | $c_{lat}$ | [9.5, 12.5] | 11.02 | mm | Lateral support spacing |
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| `whiffle_min` | $w_{min}$ | [35, 55] | 40.55 | mm | Whiffle tree minimum |
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| `whiffle_outer_to_vertical` | $\theta_w$ | [68, 80] | 75.67 | deg | Outer whiffle angle |
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| `whiffle_triangle_closeness` | $c_w$ | [50, 65] | 60.00 | mm | Whiffle triangle spacing |
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| `blank_backface_angle` | $\beta$ | [4.0, 5.0] | 4.23 | deg | Mirror backface angle (mass driver) |
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| `inner_circular_rib_dia` | $D_{rib}$ | [480, 620] | 534.00 | mm | Inner rib diameter |
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**Design Space**:
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$$\mathbf{x} = [\alpha_{in}, \alpha_{out}, p_{out}, p_{in}, p_{mid}, c_{lat}, w_{min}, \theta_w, c_w, \beta, D_{rib}]^T \in \mathbb{R}^{11}$$
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### 2.4 Mass Constraint
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| Constraint | Type | Formula | Threshold | Handling |
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|------------|------|---------|-----------|----------|
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| `mass_limit` | upper_bound | $m(\mathbf{x}) \leq m_{max}$ | 99 kg | Penalty in objective |
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**Penalty Function**:
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$$P_{mass}(\mathbf{x}) = \begin{cases}
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0 & \text{if } m \leq 99 \\
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100 \cdot (m - 99) & \text{if } m > 99
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\end{cases}$$
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**Mass Estimation** (from `blank_backface_angle`):
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$$\hat{m}(\beta) = 105 - 15 \cdot (\beta - 4.0) \text{ kg}$$
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---
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## 3. Optimization Algorithm
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### 3.1 Adaptive Hybrid Strategy
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| Parameter | Value | Description |
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|-----------|-------|-------------|
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| Algorithm | Adaptive Hybrid | FEA + Neural Surrogate |
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| Surrogate | Tuned Ensemble (3 models) | Auto-tuned architecture |
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| Sampler | TPE | Tree-structured Parzen Estimator |
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| Max Iterations | 100 | Adaptive loop iterations |
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| FEA Batch Size | 5 | Real FEA evaluations per iteration |
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| NN Trials | 1000 | Surrogate evaluations per iteration |
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| Patience | 5 | Early stopping threshold |
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| Convergence | 0.3 nm | Objective improvement threshold |
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### 3.2 Hyperparameter Tuning
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| Setting | Value |
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|---------|-------|
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| Tuning Trials | 30 |
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| Cross-Validation | 5-fold |
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| Search Space | Hidden dims, dropout, learning rate |
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| Ensemble Size | 3 models |
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| MC Dropout Samples | 30 |
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**Tuned Architecture**:
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```
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Input(11) → Linear(128) → ReLU → Dropout →
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Linear(256) → ReLU → Dropout →
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Linear(256) → ReLU → Dropout →
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Linear(128) → ReLU → Dropout →
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Linear(64) → ReLU → Linear(4)
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```
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### 3.3 Adaptive Loop Flow
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```
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┌─────────────────────────────────────────────────────────────────────────┐
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│ ADAPTIVE ITERATION k │
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├─────────────────────────────────────────────────────────────────────────┤
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│ │
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│ 1. SURROGATE EXPLORATION (1000 trials) │
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│ ├── Sample 11 design variables via TPE │
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│ ├── Predict objectives with ensemble (mean + uncertainty) │
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│ └── Select top candidates (exploitation) + diverse (exploration) │
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│ │
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│ 2. FEA VALIDATION (5 trials) │
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│ ├── Run NX Nastran SOL 101 (4 subcases) │
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│ ├── Extract Zernike coefficients from OP2 │
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│ ├── Compute relative filtered RMS │
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│ └── Store in Optuna database │
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│ │
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│ 3. SURROGATE RETRAINING │
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│ ├── Load all FEA data from database │
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│ ├── Retrain ensemble with new data │
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│ └── Update uncertainty estimates │
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│ │
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│ 4. CONVERGENCE CHECK │
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│ ├── Δbest < 0.3 nm for patience=5 iterations? │
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│ └── If converged → STOP, else → next iteration │
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│ │
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└─────────────────────────────────────────────────────────────────────────┘
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```
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---
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## 4. Simulation Pipeline
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### 4.1 FEA Trial Execution Flow
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```
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┌─────────────────────────────────────────────────────────────────────────┐
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│ FEA TRIAL n EXECUTION │
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├─────────────────────────────────────────────────────────────────────────┤
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│ │
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│ 1. CANDIDATE SELECTION │
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│ Hybrid strategy: 70% exploitation (best NN predictions) │
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│ 30% exploration (uncertain regions) │
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│ │
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│ 2. NX PARAMETER UPDATE │
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│ Module: optimization_engine/nx_solver.py │
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│ Target Part: M1_Blank.prt (and related components) │
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│ Action: Update 11 expressions with new design values │
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│ │
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│ 3. NX SIMULATION (Nastran SOL 101 - 4 Subcases) │
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│ Module: optimization_engine/solve_simulation.py │
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│ Input: ASSY_M1_assyfem1_sim1.sim │
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│ Subcases: │
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│ 1 = 90° zenith (polishing/manufacturing) │
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│ 2 = 20° zenith (reference) │
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│ 3 = 40° zenith (operational target 1) │
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│ 4 = 60° zenith (operational target 2) │
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│ Output: .dat, .op2, .f06 │
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│ │
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│ 4. ZERNIKE EXTRACTION │
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│ Module: optimization_engine/extractors/extract_zernike.py │
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│ a. Read node coordinates from BDF/DAT │
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│ b. Read Z-displacements from OP2 for each subcase │
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│ c. Compute RELATIVE displacement (target - reference) │
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│ d. Convert to WFE: W = 2 × Δδz × 10⁶ nm │
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│ e. Fit 50 Zernike coefficients via least-squares │
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│ f. Compute filtered RMS (exclude J1-J4) │
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│ │
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│ 5. MASS EXTRACTION │
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│ Module: optimization_engine/extractors/extract_mass_from_expression │
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│ Expression: p173 (CAD mass property) │
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│ │
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│ 6. OBJECTIVE COMPUTATION │
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│ rel_filtered_rms_40_vs_20 ← Zernike RMS (subcase 3 - 2) │
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│ rel_filtered_rms_60_vs_20 ← Zernike RMS (subcase 4 - 2) │
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│ mfg_90_optician_workload ← Zernike RMS J4+ (subcase 1 - 2) │
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│ │
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│ 7. WEIGHTED OBJECTIVE + MASS PENALTY │
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│ J = Σ (weight × objective / target) + mass_penalty │
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│ │
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│ 8. STORE IN DATABASE │
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│ Optuna SQLite: 3_results/study.db │
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│ User attrs: trial_source='fea', mass_kg, all Zernike coefficients │
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│ │
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└─────────────────────────────────────────────────────────────────────────┘
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```
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### 4.2 Subcase Configuration
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| Subcase | Zenith Angle | Gravity Direction | Role |
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|---------|--------------|-------------------|------|
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| 1 | 90° | Horizontal | Manufacturing/polishing reference |
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| 2 | 20° | Near-vertical | Operational reference (baseline) |
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| 3 | 40° | Mid-elevation | Operational target 1 |
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| 4 | 60° | Low-elevation | Operational target 2 |
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---
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## 5. Result Extraction Methods
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### 5.1 Zernike WFE Extraction
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| Attribute | Value |
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|-----------|-------|
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| **Extractor** | `ZernikeExtractor` |
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| **Module** | `optimization_engine.extractors.extract_zernike` |
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| **Method** | `extract_relative()` |
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| **Geometry Source** | `.dat` (BDF format, auto-detected) |
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| **Displacement Source** | `.op2` (OP2 binary) |
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| **Output** | 50 Zernike coefficients + RMS metrics per subcase pair |
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**Algorithm**:
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1. Load node coordinates $(X_i, Y_i)$ from BDF
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2. Load Z-displacements $\delta_{z,i}$ from OP2 for each subcase
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3. Compute relative displacement (node-by-node):
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$$\Delta\delta_{z,i} = \delta_{z,i}^{target} - \delta_{z,i}^{reference}$$
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4. Convert to WFE:
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$$W_i = 2 \cdot \Delta\delta_{z,i} \cdot 10^6 \text{ nm}$$
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5. Fit Zernike coefficients via least-squares:
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$$\min_{\mathbf{Z}} \| \mathbf{W} - \mathbf{P} \mathbf{Z} \|^2$$
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6. Compute filtered RMS:
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$$\sigma_{filtered} = \sqrt{\sum_{j=5}^{50} Z_j^2}$$
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**Code**:
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```python
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from optimization_engine.extractors import ZernikeExtractor
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extractor = ZernikeExtractor(op2_file, bdf_file)
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result = extractor.extract_relative(
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target_subcase="3", # 40 deg
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reference_subcase="2", # 20 deg
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displacement_unit="mm"
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)
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filtered_rms = result['relative_filtered_rms_nm'] # nm
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```
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### 5.2 Mass Extraction
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| Attribute | Value |
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|-----------|-------|
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| **Extractor** | `extract_mass_from_expression` |
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| **Module** | `optimization_engine.extractors` |
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| **Expression** | `p173` (CAD mass property) |
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| **Output** | kg |
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**Code**:
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```python
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from optimization_engine.extractors import extract_mass_from_expression
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mass_kg = extract_mass_from_expression(model_file, expression_name="p173")
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```
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---
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## 6. Neural Acceleration (Tuned Ensemble Surrogate)
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### 6.1 Configuration
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| Setting | Value | Description |
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|---------|-------|-------------|
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| `enabled` | `true` | Neural surrogate active |
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| `model_type` | `TunedEnsembleSurrogate` | Ensemble of tuned networks |
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| `ensemble_size` | 3 | Number of models in ensemble |
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| `hidden_dims` | `[128, 256, 256, 128, 64]` | Auto-tuned architecture |
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| `dropout` | 0.1 | Regularization |
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| `learning_rate` | 0.001 | Adam optimizer |
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| `batch_size` | 16 | Mini-batch size |
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| `mc_dropout_samples` | 30 | Monte Carlo uncertainty |
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### 6.2 Hyperparameter Tuning
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| Parameter | Search Space |
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|-----------|--------------|
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| `n_layers` | [3, 4, 5, 6] |
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| `hidden_dim` | [64, 128, 256, 512] |
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| `dropout` | [0.0, 0.1, 0.2, 0.3] |
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| `learning_rate` | [1e-4, 1e-3, 1e-2] |
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| `batch_size` | [8, 16, 32, 64] |
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**Tuning Objective**:
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$$\mathcal{L}_{tune} = \frac{1}{K} \sum_{k=1}^{K} MSE_{val}^{(k)}$$
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Using 5-fold cross-validation.
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### 6.3 Surrogate Model
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**Input**: $\mathbf{x} = [11 \text{ design variables}]^T \in \mathbb{R}^{11}$
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**Output**: $\hat{\mathbf{y}} = [4 \text{ objectives/constraints}]^T \in \mathbb{R}^{4}$
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- `rel_filtered_rms_40_vs_20` (nm)
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- `rel_filtered_rms_60_vs_20` (nm)
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- `mfg_90_optician_workload` (nm)
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- `mass_kg` (kg)
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**Ensemble Prediction**:
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$$\hat{y} = \frac{1}{M} \sum_{m=1}^{M} f_m(\mathbf{x})$$
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**Uncertainty Quantification** (MC Dropout):
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$$\sigma_y^2 = \frac{1}{T} \sum_{t=1}^{T} f_{dropout}^{(t)}(\mathbf{x})^2 - \hat{y}^2$$
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### 6.4 Training Data Location
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```
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m1_mirror_adaptive_V12/
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├── 2_iterations/
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│ ├── iter_001/ # Iteration 1 working files
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│ ├── iter_002/
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│ └── ...
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├── 3_results/
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│ ├── study.db # Optuna database (all trials)
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│ ├── optimization.log # Detailed log
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│ ├── surrogate_best.pt # Best tuned model weights
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│ └── tuning_results.json # Hyperparameter tuning history
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```
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### 6.5 Expected Performance
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| Metric | Value |
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|--------|-------|
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| Source Data | V11: 107 FEA samples |
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| FEA time per trial | 10-15 min |
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| Neural time per trial | ~5 ms |
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| Speedup | ~120,000x |
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| Expected R² | > 0.90 (after tuning) |
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| Uncertainty Coverage | ~95% (ensemble + MC dropout) |
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---
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## 7. Study File Structure
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```
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m1_mirror_adaptive_V12/
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│
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├── 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.*
|
||||
Reference in New Issue
Block a user