aprender-simulate 0.30.0

Unified Simulation Engine for the Sovereign AI Stack
Documentation 
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# Bayesian Optimization Verification Experiment
# EDD-compliant experiment specification

experiment_version: "1.0"
experiment_id: "EXP-BO-001"

metadata:
  name: "Bayesian Optimization Verification"
  description: |
    Verify GP surrogate and Expected Improvement acquisition function
    on the Branin benchmark function.
  author: "PAIML Engineering"
  created: "2025-12-11"
  tags: ["optimization", "bayesian", "gaussian-process", "verification"]

equation_model_card:
  emc_ref: "optimization/bayesian_optimization"
  emc_version: "1.0.0"

hypothesis:
  null_hypothesis: |
    H₀: Bayesian optimization with GP surrogate and Expected Improvement
    fails to find global minimum of Branin function within 50 evaluations.
  alternative_hypothesis: |
    H₁: BO finds a point within 0.01 of global minimum value.
  expected_outcome: "reject"  # BO should succeed

reproducibility:
  seed: 2718281828
  ieee_strict: true

simulation:
  objective:
    name: "branin"
    # f(x,y) = a(y - bx² + cx - r)² + s(1-t)cos(x) + s
    parameters:
      a: 1.0
      b: 0.12918450914398066  # 5.1/(4π²)
      c: 1.5915494309189535   # 5/π
      r: 6.0
      s: 10.0
      t: 0.039788735772973836 # 1/(8π)
    bounds: [[-5, 10], [0, 15]]
    global_minimum: 0.397887
    global_minimizers:
      - [-3.14159, 12.275]
      - [3.14159, 2.275]
      - [9.42478, 2.475]

  surrogate:
    type: "gaussian_process"
    kernel: "matern_5_2"
    noise: 1e-6
    normalize_y: true

  acquisition:
    type: "expected_improvement"
    xi: 0.01  # Exploration-exploitation tradeoff
    optimizer: "l_bfgs_b"
    n_restarts: 10

  initial_design:
    type: "latin_hypercube"
    n_points: 5

  budget: 50
  replications: 30

falsification:
  import_from_emc: true
  criteria:
    - id: "BO-OPT"
      name: "Optimization success"
      condition: "best_observed - global_minimum < tolerance"
      tolerance: 0.01
      severity: "critical"

    - id: "BO-REGRET"
      name: "Simple regret"
      condition: "simple_regret < 0.1"
      severity: "major"

    - id: "BO-CUMREGRET"
      name: "Cumulative regret"
      condition: "cumulative_regret / budget < 1.0"
      severity: "minor"

  jidoka:
    enabled: true
    stop_on_severity: "critical"

verification:
  gp_validation:
    - name: "predictive_coverage"
      description: "95% CI should contain true value ~95% of time"
      expected_coverage: 0.95
      tolerance: 0.05

    - name: "nlpd"
      description: "Negative log predictive density"
      type: "scoring_rule"

  acquisition_validation:
    - name: "ei_positive"
      description: "EI should be non-negative"
      condition: "all(ei >= 0)"

statistics:
  success_rate:
    threshold: 0.01
    confidence: 0.95

  convergence_curve:
    type: "median_with_quantiles"
    quantiles: [0.25, 0.75]

reporting:
  format: "markdown"
  output: "reports/bayesian_optimization.md"
  include:
    - "convergence_curve"
    - "gp_surface_plot"
    - "acquisition_evolution"