Atomizer/docs/06_PROTOCOLS_DETAILED/PROTOCOL_13_ADAPTIVE_MULTI_OBJECTIVE.md

Protocol 13: Adaptive Multi-Objective Optimization

Overview

Protocol 13 implements an adaptive multi-objective optimization strategy that combines:

• FEA (Finite Element Analysis) for ground truth simulations
• Neural Network Surrogates for rapid exploration
• Iterative refinement with periodic retraining

This protocol is ideal for expensive simulations where each FEA run takes significant time (minutes to hours), but you need to explore a large design space efficiently.

When to Use Protocol 13

Scenario	Recommended
FEA takes > 5 minutes per run	Yes
Need to explore > 100 designs	Yes
Multi-objective optimization (2-4 objectives)	Yes
Single objective, fast FEA (< 1 min)	No, use Protocol 10/11
Highly nonlinear response surfaces	Yes, with more FEA samples

Architecture

┌─────────────────────────────────────────────────────────────────┐
│                    Adaptive Optimization Loop                    │
├─────────────────────────────────────────────────────────────────┤
│                                                                  │
│  Iteration 1:                                                    │
│  ┌──────────────┐    ┌──────────────┐    ┌──────────────┐       │
│  │ Initial FEA  │ -> │ Train NN     │ -> │ NN Search    │       │
│  │ (50-100)     │    │ Surrogate    │    │ (1000 trials)│       │
│  └──────────────┘    └──────────────┘    └──────────────┘       │
│                                                 │                │
│                                                 v                │
│  Iteration 2+:                                                   │
│  ┌──────────────┐    ┌──────────────┐    ┌──────────────┐       │
│  │ Validate Top │ -> │ Retrain NN   │ -> │ NN Search    │       │
│  │ NN with FEA  │    │ with new data│    │ (1000 trials)│       │
│  └──────────────┘    └──────────────┘    └──────────────┘       │
│                                                                  │
└─────────────────────────────────────────────────────────────────┘

Configuration

optimization_config.json

{
  "study_name": "my_adaptive_study",
  "protocol": 13,

  "adaptive_settings": {
    "enabled": true,
    "initial_fea_trials": 50,
    "nn_trials_per_iteration": 1000,
    "fea_validation_per_iteration": 5,
    "max_iterations": 10,
    "convergence_threshold": 0.01,
    "retrain_epochs": 100
  },

  "objectives": [
    {
      "name": "thermal_40_vs_20",
      "direction": "minimize",
      "weight": 1.0
    },
    {
      "name": "thermal_60_vs_20",
      "direction": "minimize",
      "weight": 0.5
    },
    {
      "name": "manufacturability",
      "direction": "minimize",
      "weight": 0.3
    }
  ],

  "design_variables": [
    {
      "name": "rib_thickness",
      "expression_name": "rib_thickness",
      "min": 5.0,
      "max": 15.0,
      "baseline": 10.0
    }
  ],

  "surrogate_settings": {
    "enabled": true,
    "model_type": "neural_network",
    "hidden_layers": [128, 64, 32],
    "learning_rate": 0.001,
    "batch_size": 32
  }
}

Key Parameters

Parameter	Description	Recommended
initial_fea_trials	FEA runs before first NN training	50-100
nn_trials_per_iteration	NN-predicted trials per iteration	500-2000
fea_validation_per_iteration	Top NN trials validated with FEA	3-10
max_iterations	Maximum adaptive iterations	5-20
convergence_threshold	Stop if improvement < threshold	0.01 (1%)

Workflow

Phase 1: Initial FEA Sampling

# Generates space-filling Latin Hypercube samples
# Runs FEA on each sample
# Stores results in Optuna database with source='FEA'

Phase 2: Neural Network Training

# Extracts all FEA trials from database
# Normalizes inputs (design variables) to [0, 1]
# Trains multi-output neural network
# Validates on held-out set (20%)

Phase 3: NN-Accelerated Search

# Uses trained NN as objective function
# Runs NSGA-II with 1000+ trials (fast, ~ms per trial)
# Identifies Pareto-optimal candidates
# Stores predictions with source='NN'

Phase 4: FEA Validation

# Selects top N NN predictions
# Runs actual FEA on these candidates
# Updates database with ground truth
# Checks for improvement

Phase 5: Iteration

# If improved: retrain NN with new FEA data
# If converged: stop and report best
# Otherwise: continue to next iteration

Output Files

studies/my_study/
├── 3_results/
│   ├── study.db                 # Optuna database (all trials)
│   ├── adaptive_state.json      # Current iteration state
│   ├── surrogate_model.pt       # Trained neural network
│   ├── training_history.json    # NN training metrics
│   └── STUDY_REPORT.md          # Generated summary report

adaptive_state.json

{
  "iteration": 3,
  "total_fea_count": 103,
  "total_nn_count": 3000,
  "best_weighted": 1.456,
  "best_params": {
    "rib_thickness": 8.5,
    "...": "..."
  },
  "history": [
    {"iteration": 1, "fea_count": 50, "nn_count": 1000, "improved": true},
    {"iteration": 2, "fea_count": 55, "nn_count": 2000, "improved": true},
    {"iteration": 3, "fea_count": 103, "nn_count": 3000, "improved": false}
  ]
}

Dashboard Integration

Protocol 13 studies display in the Atomizer dashboard with:

• FEA vs NN Differentiation: Blue circles for FEA, orange crosses for NN
• Pareto Front Highlighting: Green markers for Pareto-optimal solutions
• Convergence Plot: Shows optimization progress with best-so-far line
• Parallel Coordinates: Filter and explore the design space
• Parameter Importance: Correlation-based sensitivity analysis

Best Practices

1. Initial Sampling Strategy

Use Latin Hypercube Sampling (LHS) for initial FEA trials to ensure good coverage:

sampler = optuna.samplers.LatinHypercubeSampler(seed=42)

2. Neural Network Architecture

For most problems, start with:

• 2-3 hidden layers
• 64-128 neurons per layer
• ReLU activation
• Adam optimizer with lr=0.001

3. Validation Strategy

Always validate top NN predictions with FEA before trusting them:

• NN predictions can be wrong in unexplored regions
• FEA validation provides ground truth
• More FEA = more accurate NN (trade-off with time)

4. Convergence Criteria

Stop when:

• No improvement for 2-3 consecutive iterations
• Reached FEA budget limit
• Objective improvement < 1% threshold

Example: M1 Mirror Optimization

# Start adaptive optimization
cd studies/m1_mirror_adaptive_V11
python run_optimization.py --start

# Monitor progress
python run_optimization.py --status

# Generate report
python generate_report.py

Results after 3 iterations:

• 103 FEA trials
• 3000 NN trials
• Best thermal 40°C vs 20°C: 5.99 nm RMS
• Best thermal 60°C vs 20°C: 14.02 nm RMS

Troubleshooting

NN Predictions Don't Match FEA

• Increase initial FEA samples
• Add more hidden layers
• Check for outliers in training data
• Ensure proper normalization

Optimization Not Converging

• Increase NN trials per iteration
• Check objective function implementation
• Verify design variable bounds
• Consider adding constraints

Memory Issues

• Reduce nn_trials_per_iteration
• Use batch processing for large datasets
• Clear trial cache periodically

Related Documentation

• Protocol 11: Multi-Objective NSGA-II
• Protocol 12: Hybrid FEA/NN
• Neural Surrogate Training
• Zernike Extractor