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

1. After user runs simulations and provides outputs, summarize sensitivity:

bash python3 scripts/sensitivity_summary.py --scores 0.7,0.3 --names conductivity,diffusivity --json

1. 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