Parameter optimization

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

# 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:

   python3 scripts/doe_generator.py --params 2 --budget 30 --method lhs --json
   

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

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

5. Recommend optimizer:

   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