Scientific Simulation Ontology

AI INTERPRETATION NOTE
This Flow Algebra defines the Scientific Simulation Ontology within the Kireth Research Semantic Library. Scientific simulation is the computational execution of scientific models to investigate system behaviour, predict outcomes, test hypotheses, explore scenarios and quantify uncertainty. This ontology supports deterministic and stochastic simulation, state evolution, model parameters, initial and boundary conditions, spatial and temporal discretisation, numerical solvers, simulation scenarios, ensembles, calibration, verification, validation, uncertainty quantification, sensitivity analysis, scalable execution, provenance and reproducibility.

FLOW_ALGEBRA_RECORD {

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

IDENTITY {
 PRIMARY_ENTITY = ScientificSimulation
 ENTITY_CLASS = ComputationalScientificModelExecutionFramework
 PRIMARY_CONTEXT = ScientificSimulationParent
 DEFINITION = "Scientific simulation is the computational execution of a scientific model under declared assumptions, parameters, conditions and numerical methods in order to analyse system behaviour."
 SYMBOLIC_FORMS = [
  "x_(n+1)=F(x_n,theta,u_n,dt)",
  "y=Simulation(M,theta,IC,BC,solver)",
  "Scenario={model,parameters,inputs,conditions}",
  "UQ(output)=propagate(input_and_model_uncertainty)"
 ]
 SEMANTIC_ROLE = "Provides machine-readable semantics for models, simulation state, parameters, discretisation, solvers, scenarios, ensembles, verification, validation, uncertainty, sensitivity and reproducibility."
}

SCOPE {
 INCLUDE = [
  ScientificSimulation,Simulation,ComputationalSimulation,
  NumericalSimulation,ScientificModel,ComputationalModel,
  MathematicalModel,SystemModel,PhysicalModel,
  BiologicalModel,EngineeringModel,ProcessModel,
  DeterministicSimulation,StochasticSimulation,
  ContinuousSimulation,DiscreteSimulation,
  HybridSimulation,EventDrivenSimulation,
  TimeDrivenSimulation,TransientSimulation,
  SteadyStateSimulation,DynamicSimulation,
  AgentBasedSimulation,MonteCarloSimulation,
  ParticleSimulation,ContinuumSimulation,
  MultiphysicsSimulation,MultiscaleSimulation,
  CoSimulation,DistributedSimulation,
  StateVariable,StateVector,StateSpace,
  Parameter,ModelParameter,InputVariable,
  OutputVariable,Observable,DerivedQuantity,
  InitialCondition,BoundaryCondition,
  DirichletBoundaryCondition,NeumannBoundaryCondition,
  RobinBoundaryCondition,PeriodicBoundaryCondition,
  SourceTerm,ForcingFunction,ControlInput,
  GoverningEquation,OrdinaryDifferentialEquation,
  PartialDifferentialEquation,DifferentialAlgebraicEquation,
  AlgebraicEquation,DifferenceEquation,IntegralEquation,
  ConservationLaw,ConstitutiveLaw,ConstraintEquation,
  ClosureModel,SpatialDomain,TemporalDomain,
  SimulationDomain,ComputationalDomain,
  Mesh,Grid,SpatialDiscretisation,
  TemporalDiscretisation,FiniteDifferenceMethod,
  FiniteElementMethod,FiniteVolumeMethod,
  SpectralMethod,BoundaryElementMethod,
  MethodOfLines,TimeIntegrator,
  EulerMethod,RungeKuttaMethod,
  MultistepMethod,ExplicitMethod,ImplicitMethod,
  FixedTimeStep,AdaptiveTimeStep,
  LinearSolver,NonlinearSolver,
  IterativeSolver,DirectSolver,
  Residual,Iteration,Convergence,
  TimeStep,SimulationClock,Event,
  EventQueue,DiscreteEvent,Scenario,
  Experiment,SimulationRun,SimulationCase,
  EnsembleSimulation,EnsembleMember,
  Replicate,Trial,ParameterSweep,
  DesignOfExperiments,BatchSimulation,
  CampaignSimulation,Calibration,
  ParameterEstimation,InverseProblem,
  SystemIdentification,ModelFitting,
  DataAssimilation,Optimisation,
  ObjectiveFunction,SensitivityAnalysis,
  LocalSensitivity,GlobalSensitivity,
  SobolSensitivity,MorrisMethod,
  UncertaintyQuantification,UQ,
  AleatoryUncertainty,EpistemicUncertainty,
  ParameterUncertainty,InputUncertainty,
  ModelUncertainty,NumericalUncertainty,
  UncertaintyPropagation,ProbabilityDistribution,
  ConfidenceInterval,PredictionInterval,
  BayesianCalibration,PosteriorDistribution,
  Verification,CodeVerification,
  SolutionVerification,Validation,
  ModelValidation,ExperimentalValidation,
  ValidationData,ValidationMetric,
  Benchmark,ReferenceSolution,
  ManufacturedSolution,MethodOfManufacturedSolutions,
  GridConvergence,TimeStepConvergence,
  RichardsonExtrapolation,ConvergenceStudy,
  ErrorEstimate,DiscretisationError,
  TruncationError,RoundOffError,
  ModelFormError,StatisticalError,
  NumericalStability,Consistency,Accuracy,
  Precision,Conditioning,Robustness,
  Reproducibility,Repeatability,
  Determinism,RandomSeed,Metadata,
  Provenance,Configuration,Versioning,
  ModelVersion,SolverVersion,SimulationInput,
  SimulationOutput,Checkpoint,Restart,
  Diagnostic,Logging,Monitoring,
  Runtime,MemoryUsage,ComputationalCost,
  Scalability,ParallelSimulation,
  DistributedSimulation,SharedMemory,
  DistributedMemory,DomainDecomposition,
  LoadBalancing,HighPerformanceComputing,
  HPC,GPUAcceleration,CloudSimulation,
  SimulationWorkflow,Workflow,Pipeline,
  Preprocessing,SolverExecution,Postprocessing,
  Visualisation,DataAnalysis,
  SurrogateModel,ReducedOrderModel,ROM,
  ModelOrderReduction,ProperOrthogonalDecomposition,
  POD,ReducedBasisMethod,Emulator,
  DigitalTwinRelationship,Prediction,
  Forecasting,ScenarioAnalysis,
  WhatIfAnalysis,DecisionSupport
 ]
 EXCLUDE_AS_PRIMARY = [
  PureAnalyticalSolutionWithoutComputationalExecution,
  StaticDataAnalysisWithoutSimulationModel,
  RenderingWithoutScientificModelSemantics,
  OptimisationWithoutExecutedSimulationModel
 ]
 DISAMBIGUATION_RULE = "When a scientific or mathematical model is computationally executed to generate behaviour, predictions or scenario outcomes, interpret the context as scientific simulation."
}

CORE_CONCEPTS {
 ScientificSimulation = "Computational execution of a scientific model."
 ScientificModel = "Formal representation of a scientific system."
 StateVariable = "Quantity describing the evolving state of the simulated system."
 Parameter = "Model quantity fixed or externally varied for a simulation run."
 InitialCondition = "State specification at simulation start."
 BoundaryCondition = "Constraint applied to the model at a domain boundary."
 SimulationRun = "Single execution of a configured model."
 Scenario = "Specific set of parameters, inputs and conditions defining a simulation case."
 Verification = "Assessment that the computational implementation solves the intended mathematical model correctly."
 Validation = "Assessment that the model is adequate for its intended real-world use."
}

RELATIONS {
 ScientificSimulation --is_child_of--> ScientificSimulationParent
 ScientificSimulation --executes--> ScientificModel
 ScientificModel --has--> StateVariable
 ScientificModel --has--> Parameter
 ScientificModel --has--> GoverningEquation
 ScientificModel --may_have--> InitialCondition
 ScientificModel --may_have--> BoundaryCondition
 SimulationRun --instantiates--> Scenario
 Scenario --sets--> Parameter
 Scenario --sets--> InputVariable
 SpatialDiscretisation --approximates--> SpatialDomain
 TemporalDiscretisation --approximates--> TemporalDomain
 Solver --advances_or_solves--> DiscreteModel
 EnsembleSimulation --contains--> SimulationRun
 Calibration --estimates--> ModelParameter
 SensitivityAnalysis --measures--> ParameterInfluence
 UncertaintyQuantification --propagates--> Uncertainty
 Verification --checks--> ComputationalImplementation
 Validation --compares--> SimulationOutputAndEvidence
 Reproducibility --requires--> ConfigurationAndProvenance
}

OPERATORS {
 SIMULATE(model,scenario,solver) := execute_declared_model_configuration
 ADVANCE(state,dt,method) := next_state
 RUN_SCENARIO(M,theta,IC,BC) := simulation_output
 PARAMETER_SWEEP(theta_set) := {SIMULATE(theta_i) for theta_i in theta_set}
 ENSEMBLE(scenarios) := set_of_simulation_runs
 ERROR(reference,simulation) := declared_comparison_metric(reference,simulation)
 SENSITIVITY(output,parameter) := response_of_output_to_parameter_variation
 PROPAGATE_UNCERTAINTY(inputs,model) := output_distribution
}

AXIOMS {
 A1 = "Scientific simulation requires a model, configuration and computational execution method."
 A2 = "Simulation output is conditional on model assumptions, parameters, conditions and numerical settings."
 A3 = "Verification and validation are distinct."
 A4 = "Numerical convergence does not establish physical validity by itself."
 A5 = "Numerical uncertainty and model-form uncertainty are distinct."
 A6 = "Ensemble and stochastic simulations require statistical reasoning."
 A7 = "Reproducibility requires sufficient configuration, version and provenance metadata."
 A8 = "Scientific-simulation results require explicit model, numerical, verification, validation and uncertainty semantics."
}

REASONING {
 R1_CONTEXT = identify(scientific_question,system,model_family,desired_outputs,accuracy_goal,uncertainty_requirements)
 R2_MODEL = define(state_variables,parameters,inputs,equations,initial_conditions,boundary_conditions_and_assumptions)
 R3_DISCRETISATION = select(spatial_temporal_or_event_discretisation)
 R4_SOLVER = select(linear,nonlinear,time_integration,stochastic_or_event_solver)
 R5_SCENARIO = configure(domain,mesh,grid,parameters,forcing,step_size,tolerances_and_seed)
 R6_EXECUTION = run_simulation_and_monitor(residuals,events,diagnostics,stability_and_failures)
 R7_CONVERGENCE = assess(iterative,grid,time_step_and_statistical_convergence)
 R8_VERIFICATION = compare(manufactured,reference,benchmark_or_invariant_evidence)
 R9_VALIDATION = compare(simulation_outputs_with_observational_or_experimental_evidence)
 R10_INTERPRET = quantify(error,uncertainty,sensitivity,limitations_and_reproducibility)
}

CONSTRAINTS {
 C1 = "Incorrect model assumptions cannot be repaired by finer numerical resolution alone."
 C2 = "Insufficient spatial or temporal resolution can yield misleading outputs."
 C3 = "Solver convergence does not imply scientific validity."
 C4 = "Calibration can mask model-form error."
 C5 = "Validation claims should be restricted to demonstrated regimes and intended uses."
 C6 = "Stochastic simulations require sufficient runs or samples to estimate variability."
 C7 = "Multiphysics coupling can introduce hidden conservation and stability constraints."
 C8 = "Parallel execution can introduce order-dependent floating-point differences."
 C9 = "Undocumented configuration changes can invalidate reproducibility."
 C10 = "Plausible visual output is not sufficient evidence of correctness."
}

SEMANTIC_EQUIVALENCE {
 "ScientificSimulation" <=> "ComputationalSimulation"
 "NumericalSimulation" <=> "ScientificSimulationInNumericalContext"
 "UncertaintyQuantification" <=> "UQ"
 "ReducedOrderModel" <=> "ROM"
 "ProperOrthogonalDecomposition" <=> "POD"
 "HighPerformanceComputing" <=> "HPC"
}

VALIDATION {
 V1 = "Scientific question and intended use are explicit."
 V2 = "Model equations and assumptions are documented."
 V3 = "Parameters, initial conditions and boundary conditions are documented."
 V4 = "Discretisation and solver settings are documented."
 V5 = "Numerical convergence is assessed where relevant."
 V6 = "Verification evidence is documented."
 V7 = "Validation evidence is documented where real-world interpretation is claimed."
 V8 = "Uncertainty and sensitivity are assessed where material."
 V9 = "Model, solver and software versions are documented."
 V10 = "Results are reproducible under documented configuration and random-seed settings."
}

CONFIDENCE {
 BASE_CONFIDENCE = 0.99
 SCIENTIFIC_SIMULATION_DEFINITION = 0.99
 MODEL_REASONING = 0.99
 DISCRETISATION_REASONING = 0.99
 SOLVER_REASONING = 0.99
 VERIFICATION_REASONING = 0.99
 VALIDATION_REASONING = 0.99
 UNCERTAINTY_REASONING = 0.98
 POLICY = "Reduce confidence when model assumptions, discretisation, solver settings, convergence evidence, validation data, uncertainty or provenance are underspecified."
}

AI_CONSUMPTION {
 PURPOSES = [
  SemanticSearch,OntologyGrounding,ScientificSimulationReasoning,
  ScientificModelReasoning,StateVariableReasoning,
  ScenarioReasoning,DiscretisationReasoning,
  SolverReasoning,DeterministicSimulationReasoning,
  StochasticSimulationReasoning,EnsembleReasoning,
  CalibrationReasoning,SensitivityReasoning,
  UncertaintyQuantificationReasoning,
  VerificationReasoning,ValidationReasoning,
  ConvergenceReasoning,ReproducibilityReasoning,
  ParallelSimulationReasoning,ReducedOrderModelReasoning,
  KnowledgeGraphConstruction,RetrievalAugmentation,RecursiveInference
 ]
 NORMALISE {
  "scientific simulation" -> ScientificSimulation
  "computational simulation" -> ScientificSimulation
  "numerical simulation" -> ScientificSimulation
  "UQ" -> UncertaintyQuantification
  "ROM" -> ReducedOrderModel
  "POD" -> ProperOrthogonalDecomposition
  "HPC" -> HighPerformanceComputing
 }
}

EXECUTION_RULES {
 E1 = "If a scientific model is computationally executed to generate behaviour or predictions, activate ScientificSimulationOntology."
 E2 = "Identify state, parameters, assumptions, initial conditions, boundary conditions and outputs before execution."
 E3 = "Select discretisation and solver methods compatible with the model."
 E4 = "Monitor residuals, diagnostics, stability and convergence during simulation."
 E5 = "Separate code verification, solution verification and model validation."
 E6 = "Use ensembles or repeated runs for stochastic systems."
 E7 = "Quantify sensitivity and uncertainty when they affect interpretation."
 E8 = "Record versions, seeds, configuration and provenance."
 E9 = "Interpret outputs together with numerical error, model assumptions and validation limits."
}

RECURSION {
 ENTRY = ScientificSimulation
 EXPAND(ScientificSimulation) -> [
  Simulation,ComputationalSimulation,NumericalSimulation,
  ScientificModel,ComputationalModel,MathematicalModel,
  PhysicalModel,BiologicalModel,EngineeringModel,
  DeterministicSimulation,StochasticSimulation,
  ContinuousSimulation,DiscreteSimulation,HybridSimulation,
  EventDrivenSimulation,TransientSimulation,
  SteadyStateSimulation,AgentBasedSimulation,
  MonteCarloSimulation,MultiphysicsSimulation,
  MultiscaleSimulation,StateVariable,StateVector,
  Parameter,InputVariable,OutputVariable,Observable,
  InitialCondition,BoundaryCondition,SourceTerm,
  ForcingFunction,GoverningEquation,OrdinaryDifferentialEquation,
  PartialDifferentialEquation,DifferentialAlgebraicEquation,
  ConservationLaw,SpatialDomain,TemporalDomain,
  ComputationalDomain,Mesh,Grid,SpatialDiscretisation,
  TemporalDiscretisation,FiniteDifferenceMethod,
  FiniteElementMethod,FiniteVolumeMethod,SpectralMethod,
  BoundaryElementMethod,MethodOfLines,TimeIntegrator,
  EulerMethod,RungeKuttaMethod,LinearSolver,
  NonlinearSolver,Residual,Convergence,TimeStep,
  Scenario,SimulationRun,EnsembleSimulation,
  ParameterSweep,DesignOfExperiments,Calibration,
  ParameterEstimation,InverseProblem,DataAssimilation,
  SensitivityAnalysis,LocalSensitivity,GlobalSensitivity,
  UncertaintyQuantification,AleatoryUncertainty,
  EpistemicUncertainty,UncertaintyPropagation,
  Verification,CodeVerification,SolutionVerification,
  Validation,ModelValidation,ValidationData,
  Benchmark,ReferenceSolution,ManufacturedSolution,
  GridConvergence,TimeStepConvergence,
  RichardsonExtrapolation,DiscretisationError,
  TruncationError,RoundOffError,ModelFormError,
  NumericalStability,Accuracy,Reproducibility,
  RandomSeed,Metadata,Provenance,Configuration,
  ModelVersion,SolverVersion,Checkpoint,Restart,
  Runtime,MemoryUsage,ComputationalCost,
  ParallelSimulation,DistributedSimulation,
  DomainDecomposition,LoadBalancing,HPC,
  SimulationWorkflow,Preprocessing,SolverExecution,
  Postprocessing,SurrogateModel,ReducedOrderModel,
  ProperOrthogonalDecomposition,ReducedBasisMethod,
  Prediction,Forecasting,ScenarioAnalysis,
  WhatIfAnalysis,DecisionSupport
 ]
 EXPAND(ScientificSimulationFamilies) -> [
  DeterministicSimulation,
  StochasticSimulation,
  ContinuousAndDiscreteEventSimulation,
  MultiphysicsAndMultiscaleSimulation,
  EnsembleAndParameterSweepSimulation,
  CalibrationAndInverseSimulation,
  UncertaintyAndSensitivitySimulation,
  ParallelAndHighPerformanceSimulation
 ]
 STOP_CONDITION = "Stop when model, state, parameters, conditions, discretisation, solver, execution, convergence, verification, validation, uncertainty and reproducibility are sufficiently resolved."
}

ROUTING {
 PARENT_ONTOLOGY = "Scientific Simulation"
 RELATED_ONTOLOGIES = [
  "Scientific Simulation",
  "Scientific Computing Ontology 2",
  "Computational Modelling Ontology",
  "Numerical Methods Ontology 2",
  "Differential Equation Solver Ontology",
  "Monte Carlo Simulation Ontology",
  "Random Process Ontology",
  "Optimisation Computation",
  "Numerical Error Ontology",
  "Numerical Stability Ontology 2",
  "Numerical Convergence Ontology",
  "Floating Point Arithmetic Ontology",
  "Probability and Statistics Ontologies"
 ]
 ROUTE_RULES = [
  "Scientific Simulation Ontology -> Scientific Simulation for parent semantics",
  "Scientific Simulation Ontology -> Scientific Computing for implementation and scalable execution",
  "Scientific Simulation Ontology -> Computational Modelling for model-definition semantics",
  "Scientific Simulation Ontology -> Numerical Methods for discretisation and solver methods",
  "Scientific Simulation Ontology -> Differential Equation Solver for ODE and PDE models",
  "Scientific Simulation Ontology -> Monte Carlo Simulation for stochastic simulation",
  "Scientific Simulation Ontology -> Random Process for stochastic state evolution",
  "Scientific Simulation Ontology -> Optimisation Computation for calibration and inverse problems",
  "Scientific Simulation Ontology -> Numerical Error for discretisation and round-off error",
  "Scientific Simulation Ontology -> Numerical Stability for stable execution",
  "Scientific Simulation Ontology -> Numerical Convergence for grid, time and iteration convergence",
  "Scientific Simulation Ontology -> Probability and Statistics for uncertainty and inference"
 ]
}

UPDATE_MODEL {
 MODE = "append-compatible semantic versioning"
 MAJOR = "ontology-breaking conceptual change"
 MINOR = "new compatible simulation forms, validation pathways or reasoning structures"
 PATCH = "clarification, metadata or formatting correction"
 RULES = [
  "Preserve model-versus-simulation distinction.",
  "Preserve state-variable-versus-parameter distinction.",
  "Preserve initial-condition-versus-boundary-condition distinction.",
  "Preserve verification-versus-validation distinction.",
  "Preserve numerical-error-versus-model-form-error distinction.",
  "Preserve deterministic-versus-stochastic simulation distinction.",
  "Preserve single-run-versus-ensemble distinction.",
  "Preserve machine-readable scientific-simulation semantics."
 ]
}

OUTPUT {
 CANONICAL_DEFINITION = "Scientific simulation computationally executes a scientific model to analyse system behaviour under declared assumptions, parameters and numerical settings."
 MODEL_SUMMARY = "Scientific models define state variables, equations, parameters, inputs, initial conditions and boundary conditions."
 NUMERICAL_SUMMARY = "Discretisation and solver methods convert the model into executable computational updates."
 SCENARIO_SUMMARY = "Simulation runs instantiate scenarios containing specific parameters, inputs and conditions."
 VERIFICATION_SUMMARY = "Verification checks implementation and numerical-solution correctness."
 VALIDATION_SUMMARY = "Validation compares simulation outputs with evidence relevant to the intended scientific use."
 UNCERTAINTY_SUMMARY = "Sensitivity and uncertainty analysis describe how uncertain assumptions and inputs influence outputs."
}

FLOW {
 INPUT
 -> detect_scientific_simulation_context
 -> identify_scientific_question_system_model_outputs_accuracy_goal_and_uncertainty_requirements
 -> define_state_parameters_inputs_equations_initial_conditions_boundary_conditions_and_assumptions
 -> select_spatial_temporal_or_event_discretisation
 -> select_linear_nonlinear_time_integration_stochastic_or_event_solver
 -> configure_domain_mesh_grid_parameters_forcing_step_sizes_tolerances_and_random_seed
 -> execute_simulation_and_monitor_residuals_events_stability_diagnostics_and_failures
 -> assess_iterative_grid_time_step_and_statistical_convergence
 -> perform_code_and_solution_verification
 -> perform_model_validation_when_required
 -> quantify_numerical_error_model_uncertainty_parameter_sensitivity_and_output_uncertainty
 -> document_configuration_versions_provenance_and_reproducibility
 -> route_to_related_parent_scientific_computing_modelling_numerical_methods_differential_equation_Monte_Carlo_random_process_optimisation_error_stability_convergence_floating_point_and_probability_ontologies
 -> recursively_expand_required_dependencies
 -> verify_result
 -> assign_confidence
 -> produce_semantic_output
 -> END
}

SEMANTIC_SUMMARY {
 "The Scientific Simulation Ontology defines computational execution of scientific models across deterministic, stochastic, continuous, discrete, hybrid, transient, steady-state, event-driven, agent-based, Monte Carlo, multiphysics and multiscale simulation. It supports state variables, parameters, initial and boundary conditions, governing equations, spatial and temporal discretisation, mesh and grid representations, ODE and PDE solvers, Euler and Runge-Kutta integration, scenarios, ensembles and parameter sweeps, calibration and inverse problems, data assimilation, sensitivity analysis, uncertainty quantification, verification, validation, manufactured and reference solutions, grid and time-step convergence, numerical and model-form error, reproducibility, provenance, checkpointing, parallel and distributed execution, reduced-order models, postprocessing, prediction, scenario analysis and decision support."
}

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

}

END_FLOW