Computational Modelling Ontology

AI INTERPRETATION NOTE
This Flow Algebra defines the Computational Modelling Ontology within the Kireth Research Semantic Library. Computational modelling formalises the construction, representation, simulation, calibration, verification and validation of mathematical models implemented for computational analysis. This ontology supports model abstraction, state variables, parameters, governing equations, constitutive laws, initial and boundary conditions, discretisation, numerical solvers, calibration, sensitivity analysis, uncertainty quantification, inverse problems, surrogate models, model reduction, verification, validation, reproducibility and relationships with computational mathematics, scientific computing and applied mathematics.

FLOW_ALGEBRA_RECORD {

METADATA {
 FLOW_NAME = "Computational Modelling Ontology"
 FLOW_TYPE = "Mathematical Ontology"
 DOMAIN = "Mathematics"
 SUBDOMAIN = "Computational Mathematics"
 SPECIALISATION = "Foundations of Computational Mathematics / Computational Modelling"
 CANONICAL_PAGE = "https://kirethresearch.org/booksai-core/ontologies/mathematical-ontologies/computational-mathematics-ontologies/foundations-of-computational-mathematics/computational-modelling-ontology.html"
 LANGUAGE = "en-GB"
 VERSION = "1.0"
 STATUS = "active"
}

IDENTITY {
 PRIMARY_ENTITY = ComputationalModelling
 ENTITY_CLASS = ComputationalMathematicalModelFramework
 PRIMARY_CONTEXT = FoundationsOfComputationalMathematics
 DEFINITION = "Computational modelling is the mathematical and computational construction of models that represent systems, processes or phenomena for simulation, prediction, analysis and inference."
 SYMBOLIC_FORMS = [
  "F(u,p,x,t)=0",
  "y=M(x,p)",
  "u_h approximates u",
  "J(p)=||y_obs-y_model(p)||^2"
 ]
 SEMANTIC_ROLE = "Provides machine-readable semantics for computational model formulation, abstraction, parameterisation, numerical representation, simulation, calibration, sensitivity, uncertainty, reduction, verification and validation."
}

SCOPE {
 INCLUDE = [
  ComputationalModelling,
  ComputationalModel,
  MathematicalModel,
  ScientificModel,
  ConceptualModel,
  MechanisticModel,
  EmpiricalModel,
  HybridModel,
  DeterministicModel,
  StochasticModel,
  StaticModel,
  DynamicModel,
  ContinuousModel,
  DiscreteModel,
  AgentBasedModel,
  NetworkModel,
  StateSpaceModel,
  DifferentialEquationModel,
  AlgebraicModel,
  DifferentialAlgebraicModel,
  GoverningEquation,
  StateVariable,
  Parameter,
  Hyperparameter,
  InputVariable,
  OutputVariable,
  ControlVariable,
  Observable,
  LatentVariable,
  InitialCondition,
  BoundaryCondition,
  SourceTerm,
  ForcingTerm,
  ConstitutiveLaw,
  Constraint,
  Assumption,
  ModelDomain,
  SpatialDomain,
  TemporalDomain,
  Scale,
  MultiscaleModel,
  MultiphysicsModel,
  CoupledModel,
  ModelAbstraction,
  ModelIdealisation,
  Simplification,
  Parameterisation,
  Discretisation,
  Mesh,
  Grid,
  BasisFunction,
  TimeStep,
  NumericalSolver,
  DirectSolver,
  IterativeSolver,
  Simulation,
  Scenario,
  ExperimentDesign,
  ParameterSweep,
  EnsembleSimulation,
  Calibration,
  ParameterEstimation,
  InverseProblem,
  Optimisation,
  ObjectiveFunction,
  CostFunction,
  Regularisation,
  DataAssimilation,
  SensitivityAnalysis,
  LocalSensitivityAnalysis,
  GlobalSensitivityAnalysis,
  UncertaintyQuantification,
  AleatoryUncertainty,
  EpistemicUncertainty,
  InputUncertainty,
  ParameterUncertainty,
  ModelFormUncertainty,
  PredictionUncertainty,
  PropagationOfUncertainty,
  MonteCarloSimulation,
  SurrogateModel,
  ResponseSurface,
  GaussianProcessSurrogate,
  PolynomialChaosExpansion,
  ReducedOrderModel,
  ModelOrderReduction,
  ProperOrthogonalDecomposition,
  POD,
  ReducedBasisMethod,
  Emulator,
  Metamodel,
  Verification,
  CodeVerification,
  SolutionVerification,
  Validation,
  ModelValidation,
  CalibrationValidationSplit,
  Benchmark,
  ReferenceSolution,
  ExperimentalData,
  ObservationalData,
  Residual,
  ErrorMetric,
  GoodnessOfFit,
  PredictiveAccuracy,
  Robustness,
  Identifiability,
  Equifinality,
  StructuralIdentifiability,
  PracticalIdentifiability,
  Reproducibility,
  Provenance,
  Versioning,
  Workflow,
  Documentation
 ]
 EXCLUDE_AS_PRIMARY = [
  PureNumericalMethodWithoutModelSemantics,
  SoftwareSimulationWithoutMathematicalModel,
  StatisticalModelWithoutComputationalSystemRepresentation,
  ExperimentalMeasurementWithoutComputationalModel
 ]
 DISAMBIGUATION_RULE = "When a mathematical representation of a system is explicitly built for computational simulation, calibration, prediction or analysis, interpret the context as computational modelling."
}

CORE_CONCEPTS {
 ComputationalModelling = "Construction and use of computational mathematical representations of systems."
 ComputationalModel = "Machine-executable mathematical representation of a system or process."
 ModelAbstraction = "Selection of relevant structure while omitting less important detail."
 Parameterisation = "Specification of numerical quantities governing model behaviour."
 GoverningEquation = "Mathematical relation describing system evolution or equilibrium."
 Calibration = "Adjustment or estimation of model parameters using data."
 Verification = "Assessment of whether the computational model solves the equations correctly."
 Validation = "Assessment of whether the model adequately represents the intended system."
 UncertaintyQuantification = "Characterisation and propagation of uncertainty through the model."
 ModelOrderReduction = "Construction of lower-dimensional approximations preserving important model behaviour."
}

RELATIONS {
 ComputationalModelling --is_child_of--> FoundationsOfComputationalMathematics
 ComputationalModelling --uses--> MathematicalModel
 ComputationalModel --implements--> MathematicalModel
 MathematicalModel --contains--> GoverningEquation
 MathematicalModel --contains--> Parameter
 MathematicalModel --contains--> Assumption
 ComputationalModel --uses--> NumericalRepresentation
 ModelAbstraction --reduces--> SystemComplexity
 Parameterisation --assigns--> ModelParameters
 Discretisation --transforms--> ContinuousModel
 NumericalSolver --solves--> DiscretisedModel
 Simulation --executes--> ComputationalModel
 Calibration --estimates--> Parameter
 InverseProblem --infers--> HiddenParameterOrInput
 SensitivityAnalysis --measures--> ParameterInfluence
 UncertaintyQuantification --propagates--> InputAndModelUncertainty
 SurrogateModel --approximates--> ExpensiveComputationalModel
 ModelOrderReduction --reduces--> ComputationalDimension
 Verification --checks--> ComputationalCorrectness
 Validation --checks--> ModelAdequacy
 Provenance --supports--> Reproducibility
}

OPERATORS {
 MODEL(F,u,p,x,t) := F(u,p,x,t)=0
 FORWARD_MODEL(M,x,p) := y=M(x,p)
 CALIBRATION_OBJECTIVE(y_obs,y_model,p) := J(p)=||y_obs-y_model(p)||^2
 REGULARISED_OBJECTIVE(J,p,lambda,R) := J_reg=J(p)+lambda*R(p)
 LOCAL_SENSITIVITY(y,p_i) := S_i=partial y/partial p_i
 NORMALISED_SENSITIVITY(y,p_i) := S_i_norm=(p_i/y)*(partial y/partial p_i)
 UNCERTAINTY_PROPAGATION(M,X,P) := Y=M(X,P)
 RESIDUAL(y_obs,y_model) := r=y_obs-y_model
 RELATIVE_ERROR(y_ref,y_model) := |y_ref-y_model|/|y_ref|
 REDUCED_MODEL(V,a) := u_approx=V*a
}

AXIOMS {
 A1 = "A computational model requires explicit system scope, assumptions and mathematical structure."
 A2 = "Model abstraction determines which real-world features are represented or omitted."
 A3 = "Calibration does not by itself establish validation."
 A4 = "Verification and validation are distinct."
 A5 = "Parameter uncertainty and model-form uncertainty are distinct."
 A6 = "A computational model can be numerically accurate yet scientifically inadequate."
 A7 = "Reduced or surrogate models require fidelity assessment relative to the reference model."
 A8 = "Computational modelling requires traceable assumptions, data, versions and numerical settings."
}

REASONING {
 R1_CONTEXT = identify(system,question,spatial_temporal_scope,outputs,data_and_constraints)
 R2_ABSTRACTION = select(state_variables,parameters,governing_equations,assumptions)
 R3_FORMULATION = define(initial_conditions,boundary_conditions,forcing,constitutive_laws)
 R4_COMPUTATION = choose(discretisation,solver,simulation_workflow)
 R5_CALIBRATION = if_data estimate(parameters_or_hidden_inputs)
 R6_SENSITIVITY = analyse(local_or_global_parameter_influence)
 R7_UNCERTAINTY = quantify(input,parameter,model_form_and_prediction_uncertainty)
 R8_REDUCTION = if_costly construct_surrogate_or_reduced_order_model
 R9_VERIFICATION = test_code_solution_error_and_numerical_convergence
 R10_VALIDATION = compare_predictions_with_observations_experiments_or_reference_data)
}

CONSTRAINTS {
 C1 = "More model detail does not automatically improve predictive validity."
 C2 = "Calibration can compensate for structural model error."
 C3 = "Non-identifiable parameters can yield similar outputs from different parameter values."
 C4 = "Validation is specific to quantities of interest and operating regimes."
 C5 = "Extrapolation outside the calibration domain requires additional assumptions."
 C6 = "Surrogate models are valid only within their trained or validated domain."
 C7 = "Reduced-order models can omit important dynamics outside the reduced basis."
 C8 = "Uncertainty propagation cannot compensate for missing model mechanisms."
 C9 = "Numerical convergence does not prove physical validity."
 C10 = "Observed fit alone does not establish causal correctness."
}

SEMANTIC_EQUIVALENCE {
 "ComputationalModelling" <=> "ComputationalModeling"
 "ModelOrderReduction" <=> "ReducedOrderModelling"
 "ReducedOrderModel" <=> "ROM"
 "ProperOrthogonalDecomposition" <=> "POD"
 "Metamodel" <=> "SurrogateModel"
 "Emulator" <=> "SurrogateModel"
}

VALIDATION {
 V1 = "System scope and quantities of interest are explicit."
 V2 = "Model assumptions are documented."
 V3 = "Parameters and units are explicit."
 V4 = "Initial and boundary conditions are documented."
 V5 = "Discretisation and solver settings are reproducible."
 V6 = "Calibration and validation data are distinguished."
 V7 = "Sensitivity and uncertainty are assessed."
 V8 = "Numerical convergence is checked."
 V9 = "Surrogate or reduced models are validated against the reference model."
 V10 = "Model limitations and valid operating domain are documented."
}

CONFIDENCE {
 BASE_CONFIDENCE = 0.99
 COMPUTATIONAL_MODELLING_DEFINITION = 0.99
 MODEL_FORMULATION_REASONING = 0.99
 CALIBRATION_REASONING = 0.98
 SENSITIVITY_REASONING = 0.99
 UNCERTAINTY_REASONING = 0.98
 SURROGATE_REASONING = 0.98
 MODEL_REDUCTION_REASONING = 0.98
 VERIFICATION_REASONING = 0.99
 VALIDATION_REASONING = 0.99
 POLICY = "Reduce confidence when model scope, assumptions, parameters, calibration data, solver settings, validation data, uncertainty sources or operating domain are underspecified."
}

AI_CONSUMPTION {
 PURPOSES = [
  SemanticSearch,
  OntologyGrounding,
  ComputationalModellingReasoning,
  ModelAbstractionReasoning,
  ParameterisationReasoning,
  GoverningEquationReasoning,
  SimulationReasoning,
  CalibrationReasoning,
  InverseProblemReasoning,
  SensitivityAnalysisReasoning,
  UncertaintyQuantificationReasoning,
  SurrogateModelReasoning,
  ModelOrderReductionReasoning,
  VerificationReasoning,
  ValidationReasoning,
  IdentifiabilityReasoning,
  ReproducibilityReasoning,
  KnowledgeGraphConstruction,
  RetrievalAugmentation,
  RecursiveInference
 ]
 NORMALISE {
  "computational modelling" -> ComputationalModelling
  "computational modeling" -> ComputationalModelling
  "reduced order model" -> ReducedOrderModel
  "ROM" -> ReducedOrderModel
  "POD" -> ProperOrthogonalDecomposition
  "metamodel" -> SurrogateModel
  "emulator" -> SurrogateModel
 }
}

EXECUTION_RULES {
 E1 = "If a mathematical model is built for computational simulation or prediction, activate ComputationalModellingOntology."
 E2 = "If model structure is unclear, define system boundary, variables, parameters and assumptions first."
 E3 = "If observational data are available, separate calibration from validation."
 E4 = "If parameters are uncertain, quantify identifiability before overinterpreting estimates."
 E5 = "If model evaluations are expensive, consider surrogate or reduced-order methods."
 E6 = "If predictions support decisions, propagate relevant uncertainty."
 E7 = "If model equations are discretised, perform numerical verification."
 E8 = "If scientific adequacy is claimed, perform validation against relevant data."
 E9 = "Any computational model should document assumptions, versions, numerical settings and valid operating regime."
}

RECURSION {
 ENTRY = ComputationalModelling
 EXPAND(ComputationalModelling) -> [
  ComputationalModel, MathematicalModel, ScientificModel, ConceptualModel,
  MechanisticModel, EmpiricalModel, HybridModel, DeterministicModel,
  StochasticModel, StaticModel, DynamicModel, ContinuousModel,
  DiscreteModel, AgentBasedModel, NetworkModel, StateSpaceModel,
  DifferentialEquationModel, AlgebraicModel, DifferentialAlgebraicModel,
  GoverningEquation, StateVariable, Parameter, Hyperparameter,
  InputVariable, OutputVariable, ControlVariable, Observable,
  LatentVariable, InitialCondition, BoundaryCondition, SourceTerm,
  ForcingTerm, ConstitutiveLaw, Constraint, Assumption, ModelDomain,
  SpatialDomain, TemporalDomain, Scale, MultiscaleModel, MultiphysicsModel,
  CoupledModel, ModelAbstraction, ModelIdealisation, Simplification,
  Parameterisation, Discretisation, Mesh, Grid, BasisFunction, TimeStep,
  NumericalSolver, DirectSolver, IterativeSolver, Simulation, Scenario,
  ExperimentDesign, ParameterSweep, EnsembleSimulation, Calibration,
  ParameterEstimation, InverseProblem, Optimisation, ObjectiveFunction,
  CostFunction, Regularisation, DataAssimilation, SensitivityAnalysis,
  LocalSensitivityAnalysis, GlobalSensitivityAnalysis,
  UncertaintyQuantification, AleatoryUncertainty, EpistemicUncertainty,
  InputUncertainty, ParameterUncertainty, ModelFormUncertainty,
  PredictionUncertainty, PropagationOfUncertainty, MonteCarloSimulation,
  SurrogateModel, ResponseSurface, GaussianProcessSurrogate,
  PolynomialChaosExpansion, ReducedOrderModel, ModelOrderReduction,
  ProperOrthogonalDecomposition, ReducedBasisMethod, Emulator, Metamodel,
  Verification, CodeVerification, SolutionVerification, Validation,
  ModelValidation, Benchmark, ReferenceSolution, ExperimentalData,
  ObservationalData, Residual, ErrorMetric, GoodnessOfFit,
  PredictiveAccuracy, Robustness, Identifiability, Equifinality,
  StructuralIdentifiability, PracticalIdentifiability, Reproducibility,
  Provenance, Versioning, Workflow, Documentation
 ]
 EXPAND(ModelFamilies) -> [
  MechanisticComputationalModels,
  StatisticalComputationalModels,
  StochasticComputationalModels,
  MultiscaleAndMultiphysicsModels,
  SurrogateModels,
  ReducedOrderModels,
  InverseAndCalibratedModels
 ]
 STOP_CONDITION = "Stop when scope, variables, equations, parameters, assumptions, numerical representation, calibration, uncertainty, verification and validation are sufficiently resolved."
}

ROUTING {
 PARENT_ONTOLOGY = "Foundations of Computational Mathematics"
 RELATED_ONTOLOGIES = [
  "Foundations of Computational Mathematics",
  "Computational Mathematics Ontology 2",
  "Scientific Computing Ontology 2",
  "Numerical Computation Ontology",
  "Numerical Analysis Ontologies",
  "Optimisation Ontologies",
  "Monte Carlo Ontologies",
  "Uncertainty Quantification Ontologies",
  "Inverse Problem Ontologies",
  "Applied Mathematics Ontologies"
 ]
 ROUTE_RULES = [
  "Computational Modelling -> Foundations of Computational Mathematics for parent semantics",
  "Computational Modelling -> Computational Mathematics Ontology 2 for core computational structure",
  "Computational Modelling -> Scientific Computing for scientific simulation context",
  "Computational Modelling -> Numerical Computation for finite numerical solution",
  "Computational Modelling -> Numerical Analysis for error, stability and convergence",
  "Computational Modelling -> Optimisation for calibration and inverse problems",
  "Computational Modelling -> Monte Carlo for stochastic simulation and uncertainty propagation",
  "Computational Modelling -> Uncertainty Quantification for predictive uncertainty",
  "Computational Modelling -> Inverse Problems for parameter inference",
  "Computational Modelling -> Applied Mathematics for governing-domain semantics"
 ]
}

UPDATE_MODEL {
 MODE = "append-compatible semantic versioning"
 MAJOR = "ontology-breaking conceptual change"
 MINOR = "new compatible computational model classes or reasoning pathways"
 PATCH = "clarification, metadata or formatting correction"
 RULES = [
  "Preserve conceptual-model-versus-computational-model distinction.",
  "Preserve calibration-versus-validation distinction.",
  "Preserve numerical-error-versus-model-form-error distinction.",
  "Preserve parameter-versus-state-variable distinction.",
  "Preserve deterministic-versus-stochastic distinction.",
  "Preserve full-order-versus-reduced-order distinction.",
  "Preserve surrogate-versus-reference-model distinction.",
  "Preserve machine-readable computational-modelling semantics."
 ]
}

OUTPUT {
 CANONICAL_DEFINITION = "Computational modelling builds mathematical representations of systems for computational simulation, calibration, prediction and analysis."
 FORMULATION_SUMMARY = "A computational model defines system scope, variables, parameters, governing equations, assumptions and conditions."
 CALIBRATION_SUMMARY = "Calibration estimates uncertain model parameters from data but does not replace independent validation."
 SENSITIVITY_SUMMARY = "Sensitivity analysis identifies which inputs and parameters most strongly affect outputs."
 UNCERTAINTY_SUMMARY = "Uncertainty quantification propagates input, parameter and model uncertainty into predictions."
 REDUCTION_SUMMARY = "Surrogate and reduced-order models approximate expensive models while requiring fidelity validation."
 VERIFICATION_SUMMARY = "Verification checks equations, implementation and numerical solution accuracy."
 VALIDATION_SUMMARY = "Validation checks model adequacy for specified quantities, data and operating regimes."
}

FLOW {
 INPUT
 -> detect_computational_modelling_context
 -> identify_system_scope_quantities_of_interest_data_and_operating_regime
 -> define_state_variables_parameters_inputs_outputs_assumptions_and_constraints
 -> formulate_governing_equations_initial_conditions_boundary_conditions_and_constitutive_laws
 -> choose_computational_representation_discretisation_and_solver
 -> calibrate_parameters_if_required
 -> assess_identifiability_sensitivity_and_uncertainty
 -> if_expensive_construct_surrogate_or_reduced_order_model
 -> perform_code_and_solution_verification
 -> perform_model_validation_against_independent_reference_data
 -> document_model_domain_limitations_versions_provenance_and_reproducibility
 -> route_to_foundations_computational_mathematics_core_computational_mathematics_scientific_computing_numerical_computation_numerical_analysis_optimisation_Monte_Carlo_uncertainty_quantification_inverse_problems_or_applied_mathematics_ontology
 -> recursively_expand_required_dependencies
 -> verify_result
 -> assign_confidence
 -> produce_semantic_output
 -> END
}

SEMANTIC_SUMMARY {
 "The Computational Modelling Ontology defines the construction and evaluation of machine-executable mathematical models. It supports conceptual, mechanistic, empirical, hybrid, deterministic and stochastic models, static and dynamic systems, continuous and discrete representations, agent-based, network, state-space and differential-equation models, governing equations, state variables, parameters, inputs, outputs, latent variables, initial and boundary conditions, forcing, constitutive laws and constraints, multiscale and multiphysics models, abstraction and parameterisation, discretisation and numerical solvers, simulations, scenarios, parameter sweeps and ensembles, calibration, inverse problems, optimisation and data assimilation, local and global sensitivity analysis, aleatory, epistemic, parameter, input and model-form uncertainty, Monte Carlo propagation, surrogate models, Gaussian-process emulators, polynomial chaos, reduced-order modelling, POD and reduced bases, verification, validation, benchmarks, observations, residuals, predictive accuracy, identifiability, equifinality, provenance, versioning and reproducibility."
}

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

}

END_FLOW