Parameter Optimization

Parameter Optimization

Goal

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

Requirements

• Python 3.10+
• No external dependencies (uses Python standard library only)

Inputs to Gather

Before running any scripts, collect from the user:

Decision Guidance

Choosing a DOE Method

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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)

Factorial sizing: the factorial grid is levels evenly spaced values per parameter, producing exactly levels ** params samples. Set the resolution explicitly with --levels (e.g. --params 2 --levels 4 -> 16 samples). If you use --budget instead, the script back-computes levels = round(budget ** (1/params)) and warns whenever the realized sample count differs from the requested budget (e.g. --budget 20 --params 2 realizes 16 samples). For an exact design, pass a perfect power (--budget 16) or, preferably, --levels.

Choosing an Optimizer

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Is dimension <= 10 AND budget <= 100?
├── YES → Bayesian Optimization
└── NO → Is dimension <= 20?
    ├── YES → CMA-ES
    └── NO → Random Search with screening

Script Outputs (JSON Fields)

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

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

# Full factorial with 4 levels per parameter (2 params -> 16 samples)
python3 scripts/doe_generator.py --params 2 --levels 4 --method factorial --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:

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

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

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

5. Recommend optimizer:

   bashCopy code
   python3 scripts/optimizer_selector.py --dim 2 --budget 30 --noise low --json
   

Error Handling

Verification checklist

• Recorded the exact doe_generator.py coverage.count and confirmed it matches the intended design — for factorial, verified count == levels ** params and that no note/requested_budget mismatch warning was emitted (or that the realized count is acceptable).
• Confirmed the chosen --method matches the Decision Guidance for the actual dimension/goal, and that quasi-random was used instead of the deprecated sobol alias (no DeprecationWarning in output).
• Recorded the optimizer_selector.py recommended strategy and expected_evals, and verified expected_evals <= budget so the plan is feasible within the stated evaluation budget.
• Logged the sensitivity_summary.py ranking and checked whether the top sensitivity is < 0.1 (the "All sensitivities are low" note); if so, did not over-interpret the ranking and revisited the output metric.
• For surrogate fits, judged quality with metrics.cv_error (leave-one-out), NOT in-sample mse — especially for rbf, where mse is near zero by construction — and compared cv_error against metrics.output_variance to confirm the surrogate beats the constant-mean baseline.
• Confirmed any reported cv_error is a finite number (not NaN), i.e. there were enough samples for leave-one-out (poly: n > degree+1; rbf: n >= 3).

Common pitfalls & rationalizations

Security

Input Validation

• sensitivity_summary.py validates --names against [a-zA-Z_][a-zA-Z0-9_ .-]* with a 200-char limit, preventing shell metacharacter injection via crafted parameter names
• All numeric list inputs are validated as finite numbers (NaN/Inf rejected)
• Comma-separated value lists are capped (10,000 for scores, 100,000 for surrogate data) to prevent resource exhaustion
• doe_generator.py caps dimension at 1,000 and budget at 1,000,000; optimizer_selector.py caps dimension at 100,000 and budget at 10,000,000
• --method is validated against a fixed allowlist (lhs, quasi-random/sobol, factorial); sobol is an accepted but deprecated alias of quasi-random
• --noise is validated against a fixed allowlist (low, medium, high)
• --model (surrogate type) is validated against a fixed allowlist (rbf, poly)
• --levels (factorial grid resolution) is validated as an integer in [2, 1000]

File Access

• Scripts read no external files; all inputs are provided via CLI arguments
• Scripts write only to stdout (JSON output); no files are created unless the agent explicitly uses the Write tool

Tool Restrictions

• Read: Used to inspect script source, references, and user data files
• Write: Used to save DOE sample plans, sensitivity rankings, or optimizer recommendations; writes are scoped to the user's working directory
• Grep/Glob: Used to locate relevant files and search references
• The skill's allowed-tools excludes Bash to prevent the agent from executing arbitrary commands when processing user-provided parameter names and constraints

Safety Measures

• No eval(), exec(), or dynamic code generation
• All subprocess calls use explicit argument lists (no shell=True)
• Reduced tool surface (no Bash) limits the agent to read/write operations only
• Parameter names are sanitized before use, preventing injection via crafted identifiers

Limitations

• Not for real-time optimization: Scripts provide recommendations, not live optimization loops
• Surrogate is lightweight: surrogate_builder.py fits a real 1-D least-squares polynomial (poly) or Gaussian RBF interpolant (rbf) using only the standard library and reports honest residual mse, leave-one-out cv_error, and the data output_variance; for production use scipy/scikit-learn/GPyTorch. For rbf, in-sample mse is near zero by construction (exact interpolation) — judge fit quality with cv_error
• 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

• v1.2.3 (2026-10-19): Center and scale polynomial fits and expose rank-deficient or unvalidated fits.

• v1.2.2 (2026-06-24): Added Verification checklist and Common pitfalls & rationalizations sections to drive evidence-based use of the DOE, optimizer, sensitivity, and surrogate scripts

• v1.2.0 (2026-06-23): Real surrogate fits (poly least-squares, rbf interpolation) with honest mse/cv_error/output_variance; explicit factorial --levels with budget-mismatch warnings; BO dimension cutoff harmonized to dim<=10; corrected Security/Error-Handling/output-field docs to match script behavior

• v1.1.0 (2024-12-24): Enhanced documentation, decision guidance, conversational examples

• v1.0.0: Initial release with core scripts

Numerical and evidence limits

Polynomial surrogate fits retain a centered/scaled basis and use SVD least squares. Rank failure is reported as unavailable fit metrics. Cross-validation with insufficient samples is null. Neither fit residual nor cross-validation establishes physical validity outside the sampled domain.