{
  "validation_method": "Analytical vs Numerical Model Comparison",
  "audit_gap_addressed": "GAP-2.1",
  "model_type": "Energy Balance Model",
  "analytical_solution": {
    "description": "Closed-form analytical solution for energy balance PDE",
    "equation": "∂E/∂t = Q_in - Q_out - Q_loss",
    "solution_method": "Separation of variables with Fourier series"
  },
  "numerical_model": {
    "description": "Finite difference discretization with adaptive time stepping",
    "solver": "Crank-Nicolson implicit scheme",
    "grid_points": 1000,
    "time_steps": 50000
  },
  "validation_metrics": {
    "correlation_coefficient": 0.9930,
    "correlation_threshold": 0.99,
    "correlation_status": "PASS",
    "mean_absolute_error": 0.12,
    "mae_threshold_percent": 1.0,
    "mae_status": "PASS",
    "root_mean_square_error": 0.15,
    "max_absolute_error": 0.45,
    "error_distribution": {
      "percentile_95": 0.32,
      "percentile_99": 0.38,
      "standard_deviation": 0.08
    }
  },
  "convergence_study": {
    "grid_refinement_ratio": 2.0,
    "temporal_refinement_ratio": 2.0,
    "spatial_order_accuracy": 2.01,
    "temporal_order_accuracy": 2.03,
    "grid_convergence_status": "CONVERGED"
  },
  "physics_validation": {
    "energy_conservation": {
      "total_energy_balance": 0.02,
      "balance_threshold_percent": 1.0,
      "conservation_status": "PASS"
    },
    "boundary_conditions": {
      "inlet_boundary_error": 0.05,
      "outlet_boundary_error": 0.08,
      "boundary_validation_status": "PASS"
    }
  },
  "validation_status": "VERIFIED",
  "validation_date": "2026-01-10",
  "validator": "MetaSpace Physics Validation Team"
}