Parameter Optimization

---
name: parameter-optimization
description: Explore and optimize simulation parameters via design of experiments (DOE), sensitivity analysis, and optimizer selection. Use for calibration, uncertainty studies, parameter sweeps, LHS sampling, Sobol analysis, surrogate modeling, or Bayesian optimization setup.
allowed-tools: Read, Bash, Write, Grep, Glob
---

# Parameter Optimization

## Goal

Provide a workflow to design experiments, rank parameter influence, and select optimization strategies for materials simulation calibration.

## Requirements

- Python 3.8+
- No external dependencies (uses Python standard library only)

## Inputs to Gather

Before running any scripts, collect from the user:

| Input | Description | Example |
|-------|-------------|---------|
| Parameter bounds | Min/max for each parameter with units | `kappa: [0.1, 10.0] W/mK` |
| Evaluation budget | Max number of simulations allowed | `50 runs` |
| Noise level | Stochasticity of simulation outputs | `low`, `medium`, `high` |
| Constraints | Feasibility rules or forbidden regions | `kappa + mobility < 5` |

## Decision Guidance

### Choosing a DOE Method

```
Is dimension <= 3 AND full coverage needed?
├── YES → Use factorial
└── NO → Is sensitivity analysis the goal?
    ├── YES → Use quasi-random (preferred; "sobol" is accepted but deprecated)
    └── NO → Use lhs (Latin Hypercube)
```

| Method | Best For | Avoid When |
|--------|----------|------------|
| `lhs` | General exploration, moderate dimensions (3-20) | Need exact grid coverage |
| `sobol` | Sensitivity analysis, uniform coverage | Very high dimensions (>20) |
| `factorial` | Low dimension (<4), need all corners | High dimension (exponential growth) |

### Choosing an Optimizer

```
Is dimension <= 5 AND budget <= 100?
├── YES → Bayesian Optimization
└── NO → Is dimension <= 20?
    ├── YES → CMA-ES
    └── NO → Random Search with screening
```

| Noise Level | Recommendation |
|-------------|----------------|
| Low | Gradient-based if derivatives available, else Bayesian Optimization |
| Medium | Bayesian Optimization with noise model |
| High | Evolutionary algorithms or robust Bayesian Optimization |

## Script Outputs (JSON Fields)

| Script | Output Fields |
|--------|---------------|
| `scripts/doe_generator.py` | `samples`, `method`, `coverage` |
| `scripts/optimizer_selector.py` | `recommended`, `expected_evals`, `notes` |
| `scripts/sensitivity_summary.py` | `ranking`, `notes` |
| `scripts/surrogate_builder.py` | `model_type`, `metrics`, `notes` |

## Workflow

1. **Generate DOE** with `scripts/doe_generator.py`
2. **Run simulations** at DOE sample points (user's responsibility)
3. **Summarize sensitivity** with `scripts/sensitivity_summary.py`
4. **Choose optimizer** using `scripts/optimizer_selector.py`
5. **(Optional)** Fit surrogate with `scripts/surrogate_builder.py`

## CLI Examples

```bash
# Generate 20 LHS samples for 3 parameters
python3 scripts/doe_generator.py --params 3 --budget 20 --method lhs --json

# Rank parameters by sensitivity scores
python3 scripts/sensitivity_summary.py --scores 0.2,0.5,0.3 --names kappa,mobility,W --json

# Get optimizer recommendation for 3D problem with 50 eval budget
python3 scripts/optimizer_selector.py --dim 3 --budget 50 --noise low --json

# Build surrogate model from simulation data
python3 scripts/surrogate_builder.py --x 0,1,2 --y 10,12,15 --model rbf --json
```

## Conversational Workflow Example

**User**: I need to calibrate thermal conductivity and diffusivity for my FEM simulation. I can run about 30 simulations.

**Agent workflow**:
1. Identify 2 parameters → `--params 2`
2. Budget is 30 → `--budget 30`
3. Use LHS for general exploration:
   ```bash
   python3 scripts/doe_generator.py --params 2 --budget 30 --method lhs --json
   ```
4. After user runs simulations and provides outputs, summarize sensitivity:
   ```bash
   python3 scripts/sensitivity_summary.py --scores 0.7,0.3 --names conductivity,diffusivity --json
   ```
5. Recommend optimizer:
   ```bash
   python3 scripts/optimizer_selector.py --dim 2 --budget 30 --noise low --json
   ```

## Error Handling

| Error | Cause | Resolution |
|-------|-------|------------|
| `params must be positive` | Zero or negative dimension | Ask user for valid parameter count |
| `budget must be positive` | Zero or negative budget | Ask user for realistic simulation budget |
| `method must be lhs, sobol, or factorial` | Invalid method | Use decision guidance to pick valid method |
| `scores must be comma-separated` | Malformed input | Reformat as `0.1,0.2,0.3` |

## Limitations

- **Not for real-time optimization**: Scripts provide recommendations, not live optimization loops
- **Surrogate is a placeholder**: `surrogate_builder.py` computes basic metrics; replace with actual model for production
- **No automatic simulation execution**: User must run simulations externally and provide results

## References

- `references/doe_methods.md` - Detailed DOE method comparison
- `references/optimizer_selection.md` - Optimizer algorithm details
- `references/sensitivity_guidelines.md` - Sensitivity analysis interpretation
- `references/surrogate_guidelines.md` - Surrogate model selection

## Version History

- **v1.1.0** (2024-12-24): Enhanced documentation, decision guidance, conversational examples
- **v1.0.0**: Initial release with core scripts