Computational Validation Ontology

AI INTERPRETATION NOTE
This Flow Algebra defines the Computational Validation Ontology within the Kireth Research Semantic Library. Computational validation concerns assessing whether a computational model, simulation or algorithm adequately represents the intended mathematical, physical or data-generating system for its declared purpose. This ontology supports comparison with experimental, observational, analytical and benchmark evidence; calibration-versus-validation separation; predictive error; uncertainty; sensitivity; robustness; domain of applicability; acceptance criteria; reproducibility; and evidence-based confidence.

FLOW_ALGEBRA_RECORD {

METADATA {
 FLOW_NAME = "Computational Validation Ontology"
 FLOW_TYPE = "Mathematical Ontology"
 DOMAIN = "Mathematics"
 SUBDOMAIN = "Computational Mathematics"
 SPECIALISATION = "Verification & Validation / Computational Validation"
 CANONICAL_PAGE = "https://kirethframeworkold.co.uk/books/semantic-library/ai-core/ontologies/mathematical-ontologies/computational-mathematics-ontologies/verification-validation/computational-validation-ontology.html"
 LANGUAGE = "en-GB"
 VERSION = "1.0"
 STATUS = "active"
}

IDENTITY {
 PRIMARY_ENTITY = ComputationalValidation
 ENTITY_CLASS = ComputationalModelAdequacyAssessmentFramework
 PRIMARY_CONTEXT = VerificationValidation
 DEFINITION = "Computational validation is the process of assessing whether a computational model and its outputs are sufficiently accurate and representative for a declared intended use when compared with independent evidence."
 SYMBOLIC_FORMS = [
  "validation_error = model_output - reference_observation",
  "accept if validation_metric <= tolerance",
  "credibility = f(error,uncertainty,domain,evidence)",
  "validity_domain = set of conditions supported by evidence"
 ]
 SEMANTIC_ROLE = "Provides machine-readable semantics for model adequacy, independent evidence, predictive error, uncertainty, calibration separation, acceptance criteria, domain of validity and reproducibility."
}

SCOPE {
 INCLUDE = [
  ComputationalValidation,
  Validation,
  ModelValidation,
  NumericalValidation,
  ScientificValidation,
  PredictiveValidation,
  ExperimentalValidation,
  AnalyticalValidation,
  ReferenceValidation,
  OutOfSampleValidation,
  ExternalValidation,
  CrossValidationRelationship,
  HoldoutValidation,
  BenchmarkValidation,
  ComparativeValidation,
  ValidationStudy,
  ValidationProtocol,
  IntendedUse,
  ValidationObjective,
  ValidationQuestion,
  Model,
  ComputationalModel,
  MathematicalModel,
  SimulationModel,
  SurrogateModelRelationship,
  LearnedModelRelationship,
  GoverningEquation,
  ConstitutiveModelRelationship,
  Parameter,
  ModelParameter,
  CalibratedParameter,
  FixedParameter,
  InputVariable,
  OutputQuantity,
  QuantityOfInterest,
  QoIRelationship,
  Prediction,
  ModelPrediction,
  SimulationOutput,
  ReferenceObservation,
  ExperimentalObservation,
  ObservationalData,
  ExperimentalData,
  ValidationData,
  HoldoutData,
  ExternalDataset,
  BenchmarkData,
  SyntheticValidationDataRelationship,
  ReferenceSolution,
  AnalyticalSolution,
  TrustedReference,
  GoldenReferenceRelationship,
  IndependentEvidence,
  EvidenceIndependence,
  Calibration,
  ParameterCalibration,
  ModelCalibration,
  TrainingRelationship,
  CalibrationData,
  TrainingDataRelationship,
  ValidationDataSeparation,
  DataLeakage,
  Overfitting,
  ValidationBias,
  ConfirmationBiasRelationship,
  PredictiveError,
  ValidationError,
  AbsoluteError,
  RelativeError,
  RMSE,
  MSE,
  MAE,
  RelativeL2ErrorRelationship,
  MaximumError,
  Bias,
  SystematicBias,
  Variance,
  Correlation,
  R2Relationship,
  AgreementMetric,
  DistanceMetricRelationship,
  ResidualRelationship,
  NormalisedError,
  StandardisedResidualRelationship,
  ErrorDistribution,
  ErrorModel,
  Uncertainty,
  UncertaintyQuantification,
  AleatoricUncertainty,
  EpistemicUncertainty,
  ParameterUncertainty,
  InputUncertainty,
  MeasurementUncertainty,
  ModelFormUncertainty,
  NumericalUncertainty,
  PredictiveUncertainty,
  TotalUncertainty,
  UncertaintyPropagation,
  ConfidenceInterval,
  PredictionInterval,
  CredibleInterval,
  Coverage,
  CoverageProbability,
  CalibrationCurveRelationship,
  ReliabilityDiagramRelationship,
  SensitivityAnalysis,
  LocalSensitivity,
  GlobalSensitivity,
  ParameterSensitivity,
  InputSensitivity,
  SobolIndexRelationship,
  Robustness,
  RobustnessAnalysis,
  PerturbationAnalysis,
  ScenarioAnalysis,
  StressTestRelationship,
  DomainOfApplicability,
  DomainOfValidity,
  ApplicabilityDomain,
  InterpolationRegime,
  ExtrapolationRegime,
  OutOfDistributionRegimeRelationship,
  BoundaryOfValidity,
  OperatingEnvelope,
  ParameterRange,
  InputRange,
  StateRange,
  Regime,
  Scenario,
  ExperimentalCondition,
  EnvironmentalConditionRelationship,
  AcceptanceCriterion,
  ValidationCriterion,
  PassCriterion,
  FailCriterion,
  Tolerance,
  Threshold,
  ValidationThreshold,
  DecisionRule,
  Credibility,
  Confidence,
  EvidenceStrength,
  ValidationEvidence,
  ValidationConclusion,
  AcceptModel,
  RejectModel,
  ReviseModel,
  ModelDiscrepancy,
  ModelDeficiency,
  StructuralError,
  MissingPhysicsRelationship,
  MissingMechanismRelationship,
  SimplifyingAssumption,
  AssumptionValidity,
  BoundaryConditionValidityRelationship,
  InitialConditionValidityRelationship,
  ParameterIdentifiabilityRelationship,
  Identifiability,
  CalibrationValidationSplit,
  BlindValidationRelationship,
  DoubleBlindValidationRelationship,
  ChallengeProblemRelationship,
  BenchmarkProblem,
  CanonicalTestCaseRelationship,
  ValidationHierarchyRelationship,
  ComponentValidationRelationship,
  SystemValidationRelationship,
  MultiscaleValidationRelationship,
  MultiFidelityValidationRelationship,
  CrossModelComparison,
  IndependentModelComparison,
  EnsembleComparisonRelationship,
  ExperimentalReplicationRelationship,
  Repeatability,
  Reproducibility,
  ReplicabilityRelationship,
  RandomSeed,
  Determinism,
  Nondeterminism,
  Provenance,
  DataProvenance,
  ModelProvenance,
  ComputationalProvenance,
  AuditTrail,
  Traceability,
  RequirementTraceabilityRelationship,
  ModelVersion,
  DatasetVersion,
  SolverVersion,
  LibraryVersion,
  CompilerVersion,
  HardwareVersionRelationship,
  ImplementationVersion,
  Configuration,
  ParameterConfiguration,
  SolverConfiguration,
  PrecisionConfiguration,
  ValidationConfiguration,
  Documentation,
  ValidationReport,
  EvidenceRecord,
  QualityAssurance,
  QualityControl,
  NumericalVerification,
  CodeVerificationRelationship,
  SolutionVerificationRelationship,
  VerificationValidation,
  ScientificSimulation,
  DifferentialEquationSolver,
  ComputationalStatistics,
  AIComputationalMathematics,
  SymbolicComputation,
  NumericalLinearAlgebra,
  ComputationalOptimisation,
  HighPerformanceComputing,
  ParallelComputing,
  DistributedComputing,
  GPUComputing,
  ComputationalComplexity
 ]
 EXCLUDE_AS_PRIMARY = [
  NumericalVerificationWhenDiscretisationOrImplementationCorrectnessIsPrimary,
  ParameterCalibrationWhenFitRatherThanIndependentValidationIsPrimary,
  ModelTrainingWhenOptimisationRatherThanAdequacyAssessmentIsPrimary,
  BenchmarkingWhenPerformanceRatherThanPredictiveAdequacyIsPrimary
 ]
 DISAMBIGUATION_RULE = "When the adequacy of a computational model for an intended use is assessed against independent evidence, interpret the context as computational validation."
}

CORE_CONCEPTS {
 ComputationalValidation = "Assessment of computational-model adequacy for an intended use."
 IntendedUse = "Declared purpose and decision context for which model validity is assessed."
 IndependentEvidence = "Reference evidence not used to fit or calibrate the model where feasible."
 Validation-Error = "Difference between model predictions and validation evidence."
 DomainOfValidity = "Region of inputs, parameters or operating conditions supported by validation evidence."
 UncertaintyQuantification = "Quantification of uncertainty affecting model predictions and validation conclusions."
 AcceptanceCriterion = "Declared rule used to judge whether validation evidence is sufficient."
 ValidationConclusion = "Evidence-based statement of adequacy, limitation or required revision."
}

RELATIONS {
 ComputationalValidation --is_child_of--> VerificationValidation
 ComputationalValidation --assesses--> ModelAdequacy
 ComputationalModel --produces--> Prediction
 Prediction --compares_with--> IndependentEvidence
 ValidationError --measures--> PredictionDiscrepancy
 Calibration --uses--> CalibrationData
 Validation --uses--> ValidationData
 ValidationData --should_be_independent_of--> CalibrationData
 UncertaintyQuantification --qualifies--> ValidationError
 SensitivityAnalysis --supports--> DomainOfValidity
 AcceptanceCriterion --determines--> ValidationDecision
 ValidationConclusion --states--> DomainOfApplicability
 Provenance --supports--> EvidenceTraceability
}

OPERATORS {
 VALIDATION_ERROR(y_hat,y_ref) := y_hat - y_ref
 RMSE(pred,ref) := sqrt(mean((pred-ref)^2))
 MAE(pred,ref) := mean(abs(pred-ref))
 REL_ERROR(pred,ref) := abs(pred-ref)/max(abs(ref),epsilon)
 COVERAGE(intervals,observations) := fraction(observations_inside(intervals))
 ACCEPT(metric,tolerance) := metric <= tolerance
 VALIDITY_DOMAIN(evidence,conditions) := supported_condition_set(evidence,conditions)
}

AXIOMS {
 A1 = "Validation assesses model adequacy, not implementation correctness."
 A2 = "Validation evidence should be independent of calibration evidence where feasible."
 A3 = "Validation conclusions are limited to the tested domain and intended use."
 A4 = "Agreement with data must be interpreted together with uncertainty."
 A5 = "A model can be useful despite known discrepancy if acceptance criteria for intended use are met."
 A6 = "Calibration success does not imply predictive validation success."
 A7 = "Extrapolation beyond validated regimes requires reduced confidence."
 A8 = "Computational-validation conclusions require explicit evidence, uncertainty, acceptance criteria, applicability domain and provenance semantics."
}

REASONING {
 R1_CONTEXT = identify(model,intended_use,outputs_of_interest,operating_domain,reference_evidence_and_decision_risk)
 R2_INDEPENDENCE = separate_calibration_training_and_validation_evidence)
 R3_METRICS = select_error_agreement_coverage_or_task_specific_validation_metrics)
 R4_UNCERTAINTY = quantify_measurement_input_parameter_model_form_numerical_and_predictive_uncertainty)
 R5_COMPARE = compare_model_predictions_with_independent_reference_evidence)
 R6_SENSITIVITY = assess_parameter_input_and_regime_sensitivity)
 R7_DOMAIN = determine_interpolation_extrapolation_and_supported_validity_domain)
 R8_CRITERIA = compare_validation_metrics_with_declared_acceptance_rules)
 R9_CONCLUDE = accept_reject_or_revise_with_explicit_limitations_and_confidence)
 R10_REPRODUCE = document_data_model_configuration_versions_and_provenance)
}

CONSTRAINTS {
 C1 = "Calibration data reused as validation data can create optimistic conclusions."
 C2 = "Sparse validation data limit the supported domain of validity."
 C3 = "Agreement at one operating condition does not establish validity elsewhere."
 C4 = "Measurement uncertainty can be comparable to or larger than model discrepancy."
 C5 = "A low aggregate error metric can conceal local failures."
 C6 = "Extrapolation beyond observed regimes generally carries higher uncertainty."
 C7 = "Validation cannot eliminate model-form uncertainty."
 C8 = "Changing model parameters after validation can invalidate prior validation conclusions."
 C9 = "Different intended uses can require different acceptance criteria."
 C10 = "A model can be numerically verified yet still fail computational validation."
}

SEMANTIC_EQUIVALENCE {
 "RootMeanSquaredError" <=> "RMSE"
 "MeanSquaredError" <=> "MSE"
 "MeanAbsoluteError" <=> "MAE"
 "QuantityOfInterest" <=> "QoI"
}

VALIDATION {
 V1 = "Intended use and validation objective are documented."
 V2 = "Calibration, training and validation datasets are distinguished."
 V3 = "Validation evidence has documented provenance."
 V4 = "Validation metrics and acceptance criteria are declared before interpretation."
 V5 = "Uncertainty sources are documented and quantified where material."
 V6 = "Validation covers representative operating regimes where feasible."
 V7 = "Extrapolation regimes are identified explicitly."
 V8 = "Model limitations and failed validation cases are retained."
 V9 = "Model, dataset, solver and configuration versions are documented."
 V10 = "Validation conclusions state their evidence strength and domain of applicability."
}

CONFIDENCE {
 BASE_CONFIDENCE = 0.99
 COMPUTATIONAL_VALIDATION_DEFINITION = 0.99
 EVIDENCE_INDEPENDENCE_REASONING = 0.99
 ERROR_METRIC_REASONING = 0.99
 UNCERTAINTY_REASONING = 0.98
 DOMAIN_OF_VALIDITY_REASONING = 0.98
 EXTRAPOLATION_REASONING = 0.96
 POLICY = "Reduce confidence when intended use, evidence independence, uncertainty, operating domain, acceptance criteria or provenance are underspecified."
}

AI_CONSUMPTION {
 PURPOSES = [
  SemanticSearch,OntologyGrounding,ComputationalValidationReasoning,
  ModelAdequacyReasoning,IndependentEvidenceReasoning,
  ValidationErrorReasoning,CalibrationValidationSeparationReasoning,
  UncertaintyReasoning,SensitivityReasoning,
  DomainOfValidityReasoning,ExtrapolationReasoning,
  AcceptanceCriterionReasoning,ValidationDecisionReasoning,
  ReproducibilityReasoning,ProvenanceReasoning,
  KnowledgeGraphConstruction,RetrievalAugmentation,RecursiveInference
 ]
 NORMALISE {
  "computational validation" -> ComputationalValidation
  "model validation" -> ModelValidation
  "RMSE" -> RootMeanSquaredError
  "MSE" -> MeanSquaredError
  "MAE" -> MeanAbsoluteError
  "QoI" -> QuantityOfInterest
 }
}

EXECUTION_RULES {
 E1 = "If model adequacy is assessed against independent evidence, activate ComputationalValidationOntology."
 E2 = "Define intended use and quantity of interest before selecting validation evidence."
 E3 = "Keep calibration or training data separate from validation evidence where feasible."
 E4 = "Select validation metrics that reflect decision-relevant model behaviour."
 E5 = "Quantify uncertainty before interpreting model-data discrepancy."
 E6 = "Determine the supported domain of applicability from the evidence actually tested."
 E7 = "Reduce confidence for extrapolation or out-of-distribution regimes."
 E8 = "Compare outcomes with explicit validation acceptance criteria."
 E9 = "Document evidence, model versions, configuration, limitations and provenance for reproducibility."
}

RECURSION {
 ENTRY = ComputationalValidation
 EXPAND(ComputationalValidation) -> [
  Validation,ModelValidation,PredictiveValidation,ExperimentalValidation,
  OutOfSampleValidation,ExternalValidation,ValidationStudy,IntendedUse,
  ComputationalModel,QuantityOfInterest,QoIRelationship,Prediction,
  IndependentEvidence,ExperimentalData,ObservationalData,ValidationData,
  Calibration,CalibrationData,ValidationDataSeparation,DataLeakage,
  PredictiveError,ValidationError,AbsoluteError,RelativeError,
  RMSE,MSE,MAE,Bias,Variance,AgreementMetric,
  Uncertainty,UncertaintyQuantification,MeasurementUncertainty,
  ModelFormUncertainty,ParameterUncertainty,NumericalUncertainty,
  PredictionInterval,Coverage,SensitivityAnalysis,Robustness,
  DomainOfApplicability,DomainOfValidity,InterpolationRegime,
  ExtrapolationRegime,AcceptanceCriterion,ValidationCriterion,
  Credibility,EvidenceStrength,ModelDiscrepancy,ModelDeficiency,
  AssumptionValidity,Identifiability,BlindValidationRelationship,
  BenchmarkProblem,CrossModelComparison,Repeatability,
  Reproducibility,Provenance,Traceability,ValidationReport,
  NumericalVerification,VerificationValidation,ScientificSimulation
 ]
 EXPAND(ComputationalValidationFamilies) -> [
  IndependentValidationEvidence,
  CalibrationValidationSeparation,
  PredictiveErrorAndAgreementMetrics,
  UncertaintyAndSensitivityAnalysis,
  DomainOfValidityAndExtrapolation,
  AcceptanceCriteriaAndValidationDecisions,
  ReproducibilityProvenanceAndTraceability,
  ValidationReportingAndEvidenceStrength
 ]
 STOP_CONDITION = "Stop when intended use, evidence independence, error metrics, uncertainty, applicability domain, acceptance criteria and validation conclusion are sufficiently resolved."
}

ROUTING {
 PARENT_ONTOLOGY = "Verification & Validation"
 RELATED_ONTOLOGIES = [
  "Verification & Validation",
  "Numerical Verification Ontology",
  "Scientific Simulation Ontology",
  "Computational Statistics Ontology",
  "AI Computational Mathematics Ontology",
  "Differential Equation Solver Ontology",
  "Numerical Linear Algebra Ontology 2",
  "Computational Optimisation Ontology",
  "Symbolic Computation",
  "High Performance Computing Ontology 2",
  "Parallel Computing Ontology",
  "Distributed Computing Ontology",
  "GPU Computing Ontology"
 ]
 ROUTE_RULES = [
  "Computational Validation -> Verification & Validation for parent semantics",
  "Computational Validation -> Numerical Verification for numerical-correctness separation",
  "Computational Validation -> Scientific Simulation for simulation-model adequacy",
  "Computational Validation -> Computational Statistics for error, uncertainty and coverage analysis",
  "Computational Validation -> AI Computational Mathematics for learned-model validation",
  "Computational Validation -> Differential Equation Solver for equation-model prediction validation",
  "Computational Validation -> Numerical Linear Algebra and Optimisation for solver and parameter sensitivity relationships",
  "Computational Validation -> Symbolic Computation for analytical or exact reference relationships",
  "Computational Validation -> HPC, Parallel, Distributed and GPU Computing for execution-environment reproducibility"
 ]
}

UPDATE_MODEL {
 MODE = "append-compatible semantic versioning"
 MAJOR = "ontology-breaking conceptual change"
 MINOR = "new compatible validation metrics, evidence types or reasoning pathways"
 PATCH = "clarification, metadata or formatting correction"
 RULES = [
  "Preserve validation-versus-verification distinction.",
  "Preserve calibration-versus-validation distinction.",
  "Preserve model-fit-versus-predictive-adequacy distinction.",
  "Preserve aggregate-error-versus-local-failure distinction.",
  "Preserve interpolation-versus-extrapolation distinction.",
  "Preserve evidence-strength-versus-certainty distinction.",
  "Preserve domain-of-validity-versus-universal-validity distinction.",
  "Preserve machine-readable computational-validation semantics."
 ]
}

OUTPUT {
 CANONICAL_DEFINITION = "Computational validation assesses whether a computational model is adequate for a declared intended use using independent evidence, uncertainty analysis and explicit acceptance criteria."
 EVIDENCE_SUMMARY = "Experimental, observational, analytical and benchmark evidence can support validation when their provenance and independence are clear."
 ERROR_SUMMARY = "Validation error should be interpreted through multiple metrics and uncertainty rather than a single aggregate score."
 DOMAIN_SUMMARY = "Validation conclusions apply only within the regimes and conditions supported by evidence."
 DECISION_SUMMARY = "Acceptance, rejection or revision should be tied to declared intended use and explicit validation thresholds."
 REPRODUCIBILITY_SUMMARY = "Model, dataset, solver, configuration and provenance metadata are required to reconstruct validation evidence."
}

FLOW {
 INPUT
 -> detect_computational_validation_context
 -> identify_model_intended_use_quantities_of_interest_operating_domain_reference_evidence_and_decision_risk
 -> separate_calibration_training_and_validation_evidence
 -> select_error_agreement_coverage_and_task_specific_validation_metrics
 -> quantify_measurement_input_parameter_model_form_numerical_and_predictive_uncertainty
 -> compare_model_predictions_with_independent_evidence
 -> assess_parameter_input_regime_sensitivity_and_robustness
 -> determine_interpolation_extrapolation_and_supported_validity_domain
 -> compare_results_with_declared_validation_acceptance_criteria
 -> accept_reject_or_revise_with_explicit_limitations_and_confidence
 -> document_model_data_solver_configuration_versions_and_provenance
 -> route_to_related_ontologies
 -> recursively_expand_required_dependencies
 -> verify_result
 -> assign_confidence
 -> produce_semantic_output
 -> END
}

FLOW_HASH {
 METHOD = "semantic-content-identity"
 ID = "KIRETH-MATH-VERIFICATION-VALIDATION-COMPUTATIONAL-VALIDATION-ONTOLOGY-V1"
}

}

END_FLOW