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

• Generate DOE with scripts/doe_generator.py

• Run simulations at DOE sample points (user's responsibility)

• Summarize sensitivity with scripts/sensitivity_summary.py

• Choose optimizer using scripts/optimizer_selector.py

• (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:

• Identify 2 parameters → --params 2

• Budget is 30 → --budget 30

• Use LHS for general exploration: python3 scripts/doe_generator.py --params 2 --budget 30 --method lhs --json

• After user runs simulations and provides outputs, summarize sensitivity: python3 scripts/sensitivity_summary.py --scores 0.7,0.3 --names conductivity,diffusivity --json

• 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