Parameter Sweep Ontology

AI INTERPRETATION NOTE
This Flow Algebra defines the Parameter Sweep Ontology within the Kireth Research Semantic Library. A parameter sweep is a controlled computational experiment in which one or more parameters are systematically varied across a defined search space so that model, solver, simulation or algorithm behaviour can be measured, compared, analysed and validated. This ontology supports grid sweeps, random sweeps, factorial designs, Latin hypercube sampling, adaptive sweeps, scenario enumeration, parallel execution, stopping criteria, metrics, sensitivity analysis, provenance, reproducibility and evidence-based interpretation.

FLOW_ALGEBRA_RECORD {

METADATA {
 FLOW_NAME = "Parameter Sweep Ontology"
 FLOW_TYPE = "Mathematical Ontology"
 DOMAIN = "Mathematics"
 SUBDOMAIN = "Computational Mathematics"
 SPECIALISATION = "Computational Scientific Workflows / Parameter Sweep"
 CANONICAL_PAGE = "https://kirethframeworkold.co.uk/books/semantic-library/ai-core/ontologies/mathematical-ontologies/computational-mathematics-ontologies/computational-scientific-workflows/parameter-sweep-ontology.html"
 LANGUAGE = "en-GB"
 VERSION = "1.0"
 STATUS = "active"
}

IDENTITY {
 PRIMARY_ENTITY = ParameterSweep
 ENTITY_CLASS = SystematicParameterExplorationFramework
 PRIMARY_CONTEXT = ComputationalScientificWorkflow
 DEFINITION = "A parameter sweep is a structured set of computational runs in which selected parameters are varied over a declared search space to measure the response of a model, solver, algorithm or simulation."
 SYMBOLIC_FORMS = [
  "Theta = theta_1 x theta_2 x ... x theta_n",
  "run_i = execute(model,theta_i)",
  "response_i = metric(run_i)",
  "sweep_result = {(theta_i,response_i)}"
 ]
 SEMANTIC_ROLE = "Provides machine-readable semantics for parameter spaces, sweep designs, sampling, run generation, parallel execution, response measurement, sensitivity, provenance and reproducibility."
}

SCOPE {
 INCLUDE = [
  ParameterSweep,
  ParameterStudy,
  ParameterExploration,
  ParameterScan,
  ParameterSearchRelationship,
  ComputationalExperiment,
  NumericalExperiment,
  SimulationExperiment,
  ExperimentRun,
  SweepRun,
  Parameter,
  SweepParameter,
  InputParameter,
  ModelParameter,
  SolverParameter,
  NumericalParameter,
  HyperparameterRelationship,
  FixedParameter,
  VariableParameter,
  ParameterSet,
  ParameterVector,
  ParameterTuple,
  ParameterConfiguration,
  SearchSpace,
  ParameterSpace,
  DesignSpace,
  FactorSpace,
  Domain,
  ParameterDomain,
  ContinuousDomain,
  DiscreteDomain,
  CategoricalDomainRelationship,
  IntegerDomain,
  RealDomain,
  BoundedDomain,
  UnboundedDomainRelationship,
  LowerBound,
  UpperBound,
  Interval,
  Range,
  ParameterRange,
  StepSize,
  Resolution,
  NumberOfLevels,
  FactorLevel,
  Grid,
  ParameterGrid,
  CartesianProduct,
  GridSweep,
  ExhaustiveSweep,
  FullFactorialDesign,
  FractionalFactorialDesignRelationship,
  OneFactorAtATime,
  OFAT,
  RandomSweep,
  RandomSampling,
  UniformSampling,
  StratifiedSamplingRelationship,
  LatinHypercubeSampling,
  LatinHypercube,
  SobolSequenceRelationship,
  QuasiRandomSamplingRelationship,
  LowDiscrepancySequenceRelationship,
  AdaptiveSweep,
  SequentialSweep,
  IterativeSweep,
  RefinementSweep,
  CoarseToFineSweep,
  MultiResolutionSweepRelationship,
  NestedSweep,
  ConditionalSweep,
  HierarchicalSweepRelationship,
  ScenarioSweep,
  CaseSweep,
  SeedSweep,
  SensitivitySweep,
  ToleranceSweep,
  MeshSweep,
  TimeStepSweep,
  PrecisionSweep,
  SolverSweep,
  AlgorithmSweep,
  ModelSweep,
  ArchitectureSweepRelationship,
  HyperparameterSweepRelationship,
  SweepDefinition,
  SweepSpecification,
  SweepPlan,
  SweepProtocol,
  SweepConfiguration,
  ParameterBinding,
  ParameterAssignment,
  RunGeneration,
  ConfigurationGeneration,
  CombinationGeneration,
  CandidatePoint,
  SamplePoint,
  DesignPoint,
  RunIndex,
  SweepIndex,
  RunIdentifier,
  ConfigurationIdentifier,
  BaselineConfiguration,
  ReferenceConfiguration,
  ControlConfiguration,
  DefaultConfiguration,
  Metric,
  Response,
  ResponseVariable,
  QuantityOfInterest,
  QoI,
  EvaluationMetric,
  AccuracyMetric,
  PerformanceMetric,
  ErrorMetric,
  RobustnessMetric,
  StabilityMetric,
  ConvergenceMetric,
  Runtime,
  MemoryUsage,
  Throughput,
  ObjectiveValue,
  SuccessRate,
  FailureRate,
  ResidualNorm,
  ValidationMetric,
  VerificationMetric,
  SensitivityAnalysis,
  LocalSensitivity,
  GlobalSensitivity,
  ParameterSensitivity,
  ResponseSurfaceRelationship,
  MainEffect,
  InteractionEffect,
  CorrelationRelationship,
  MonotonicityRelationship,
  ThresholdBehaviourRelationship,
  BifurcationRelationship,
  PhaseTransitionRelationship,
  StabilityRegionRelationship,
  FeasibleRegion,
  InfeasibleRegion,
  ValidRegion,
  FailureRegion,
  Constraint,
  ParameterConstraint,
  CoupledConstraint,
  ConditionalConstraint,
  FeasibilityCheck,
  ConstraintCheck,
  SkipInvalidConfiguration,
  InvalidConfiguration,
  FailedRun,
  NonconvergentRun,
  TimeoutRun,
  MissingResult,
  PartialResult,
  RunStatus,
  Pending,
  Running,
  Completed,
  Failed,
  Skipped,
  Retried,
  Cancelled,
  ParallelSweep,
  DistributedSweep,
  BatchSweep,
  EnsembleSweepRelationship,
  TaskParallelism,
  DataParallelismRelationship,
  HighPerformanceComputing,
  ParallelComputing,
  DistributedComputing,
  GPUComputing,
  ClusterComputing,
  ResourceAllocation,
  Worker,
  WorkerPoolRelationship,
  CPU,
  GPU,
  Memory,
  Storage,
  Network,
  JobScheduler,
  TaskScheduler,
  SweepScheduler,
  WorkflowScheduler,
  Orchestration,
  DynamicScheduling,
  StaticScheduling,
  LoadBalancing,
  Queue,
  QueueLengthRelationship,
  Makespan,
  Throughput,
  SchedulingOverhead,
  Checkpointing,
  SweepCheckpoint,
  RunCheckpoint,
  Resume,
  Restart,
  Retry,
  RetryPolicy,
  FaultTolerance,
  EarlyStopping,
  SweepTerminationCriterion,
  BudgetLimit,
  RunBudget,
  TimeBudget,
  ComputeBudget,
  ConvergenceOfSweepRelationship,
  CoverageCriterionRelationship,
  SaturationCriterionRelationship,
  DuplicateConfiguration,
  Deduplication,
  Cache,
  ResultCache,
  CacheKey,
  MemoisationRelationship,
  ResultReuse,
  Reproducibility,
  Repeatability,
  Determinism,
  Nondeterminism,
  RandomSeed,
  SeedControl,
  Provenance,
  SweepProvenance,
  ExperimentProvenance,
  WorkflowProvenance,
  DataProvenance,
  ModelProvenance,
  ComputationalProvenance,
  Lineage,
  AuditTrail,
  Traceability,
  SweepManifest,
  RunManifest,
  ExecutionLog,
  ResultLog,
  ErrorLog,
  ParameterLog,
  ConfigurationLog,
  SweepVersion,
  ModelVersion,
  SolverVersion,
  MethodVersion,
  DatasetVersion,
  LibraryVersion,
  CompilerVersion,
  ImplementationVersion,
  EnvironmentCapture,
  Verification,
  Validation,
  NumericalVerification,
  ComputationalValidation,
  ErrorAnalysis,
  Benchmark,
  RegressionTesting,
  VerificationMetrics,
  ValidationMetrics,
  ScientificWorkflow,
  DataPipeline,
  NumericalWorkflow,
  SimulationWorkflow,
  ComputationalExperimentOntologyRelationship,
  ScientificSimulation,
  NumericalLinearAlgebra,
  DifferentialEquationSolver,
  ComputationalOptimisation,
  ComputationalStatistics,
  AIComputationalMathematics,
  SymbolicComputation,
  ComputationalDataStructures,
  GraphAlgorithms
 ]
 EXCLUDE_AS_PRIMARY = [
  SingleRunParameterConfigurationWithoutSystematicVariation,
  OptimisationWhenSearchingDirectlyForAnOptimumIsPrimary,
  CalibrationWhenFittingParametersToEvidenceIsPrimary,
  RandomSimulationEnsembleWithoutDeclaredParameterExplorationSemantics
 ]
 DISAMBIGUATION_RULE = "When one or more parameters are systematically varied across a declared set or search space to observe computational responses, interpret the context as a parameter sweep."
}

CORE_CONCEPTS {
 ParameterSweep = "Systematic exploration of computational behaviour over parameter configurations."
 SweepParameter = "Parameter intentionally varied during the sweep."
 ParameterSpace = "Set of allowed parameter configurations."
 DesignPoint = "Specific parameter configuration evaluated by a sweep run."
 GridSweep = "Sweep over a Cartesian product of predefined parameter levels."
 RandomSweep = "Sweep using randomly sampled parameter configurations."
 SweepMetric = "Quantity used to evaluate each sweep run."
 SweepProvenance = "Traceable record of parameter definitions, generated configurations, runs and outputs."
}

RELATIONS {
 ParameterSweep --is_child_of--> ComputationalScientificWorkflow
 ParameterSweep --is_type_of--> ComputationalExperiment
 ParameterSweep --varies--> SweepParameters
 SweepParameter --belongs_to--> ParameterSpace
 ParameterSpace --contains--> DesignPoints
 SweepPlan --generates--> SweepRuns
 SweepRun --uses--> ParameterConfiguration
 SweepRun --produces--> Response
 Metric --evaluates--> SweepRun
 ParallelSweep --executes--> IndependentRunsConcurrently
 SensitivityAnalysis --uses--> SweepResults
 Provenance --records--> ParametersRunsAndResults
 Reproducibility --requires--> VersionedSweepDefinitionAndEnvironment
}

OPERATORS {
 GRID(space) := cartesian_product(parameter_levels(space))
 SAMPLE(space,n,scheme) := sample_design_points(space,n,scheme)
 GENERATE_RUN(theta) := create_run_configuration(theta)
 EXECUTE_SWEEP(points,model) := {run(model,p) for p in points}
 RESPONSE(run,metric) := metric(run)
 FILTER_VALID(points,constraints) := {p in points | satisfies(p,constraints)}
 AGGREGATE(results) := organise_by_parameter_and_metric(results)
}

AXIOMS {
 A1 = "A parameter sweep requires at least one intentionally varied parameter."
 A2 = "Every sweep run must be traceable to a unique parameter configuration."
 A3 = "Sweep design determines coverage of the parameter space."
 A4 = "Grid sweeps scale multiplicatively with the number of parameter levels."
 A5 = "Parallel execution can accelerate independent sweep runs without changing sweep semantics."
 A6 = "Invalid parameter combinations should be distinguished from failed computational runs."
 A7 = "Sweep results are observational over the sampled design and do not imply behaviour outside it."
 A8 = "Parameter-sweep conclusions require explicit parameter-space, sampling, metric, execution and provenance semantics."
}

REASONING {
 R1_CONTEXT = identify(model_or_algorithm,sweep_goal,parameters,ranges,constraints,metrics,budget_and_resources)
 R2_SPACE = define_parameter_domains_levels_bounds_and_dependencies)
 R3_DESIGN = choose_grid_random_Latin_hypercube_factorial_adaptive_or_custom_sampling)
 R4_FILTER = remove_or_mark_invalid_parameter_combinations)
 R5_GENERATE = create_unique_run_configurations_and_identifiers)
 R6_SCHEDULE = execute_runs_serially_parallel_or_distributed_under_declared_resources)
 R7_COLLECT = gather_metrics_outputs_failures_and_logs_for_each_configuration)
 R8_ANALYSE = evaluate_trends_interactions_sensitivity_feasible_regions_and_failure_boundaries)
 R9_VERIFY = apply_numerical_verification_validation_and_regression_checks_where_needed)
 R10_PROVENANCE = record_parameter_space_sampling_scheme_versions_environment_and_results)
}

CONSTRAINTS {
 C1 = "Cartesian grid size grows exponentially with the number of swept parameters."
 C2 = "Coarse grids can miss narrow transitions or failure regions."
 C3 = "Random sweeps require seed and sample-count semantics for reproducibility."
 C4 = "Invalid parameter combinations should not be confused with solver failures."
 C5 = "Unequal computational cost across configurations can bias scheduling and budget usage."
 C6 = "Adaptive sweeps depend on prior observations and therefore require sequential provenance."
 C7 = "Caching can return stale results if configuration or model versions are not part of the cache key."
 C8 = "Parameter interactions can invalidate one-factor-at-a-time interpretation."
 C9 = "Sweep coverage does not establish extrapolation outside the sampled domain."
 C10 = "Large sweeps require explicit failure, timeout and partial-result policies."
}

SEMANTIC_EQUIVALENCE {
 "OneFactorAtATime" <=> "OFAT"
 "QuantityOfInterest" <=> "QoI"
 "HighPerformanceComputing" <=> "HPC"
}

VALIDATION {
 V1 = "Sweep goal and varied parameters are documented."
 V2 = "Parameter domains, bounds and units are documented."
 V3 = "Sampling or sweep design is documented."
 V4 = "Parameter constraints and invalid combinations are explicit."
 V5 = "Each run has a unique configuration identifier."
 V6 = "Random seeds are documented for stochastic sampling."
 V7 = "Failed, skipped and nonconvergent runs are retained."
 V8 = "Metrics and aggregation rules are documented."
 V9 = "Model, solver, data and environment versions are documented."
 V10 = "Sweep results are reproducible from the recorded sweep specification and provenance."
}

CONFIDENCE {
 BASE_CONFIDENCE = 0.99
 PARAMETER_SWEEP_DEFINITION = 0.99
 PARAMETER_SPACE_REASONING = 0.99
 GRID_SWEEP_REASONING = 0.99
 RANDOM_SWEEP_REASONING = 0.98
 ADAPTIVE_SWEEP_REASONING = 0.98
 SENSITIVITY_REASONING = 0.98
 POLICY = "Reduce confidence when parameter bounds, sampling design, constraints, failed-run handling, seed control, coverage or provenance are underspecified."
}

AI_CONSUMPTION {
 PURPOSES = [
  SemanticSearch,OntologyGrounding,ParameterSweepReasoning,
  ParameterSpaceReasoning,GridSweepReasoning,
  RandomSweepReasoning,LatinHypercubeReasoning,
  FactorialDesignReasoning,AdaptiveSweepReasoning,
  ConstraintFilteringReasoning,ParallelSweepReasoning,
  SensitivityReasoning,FailureRegionReasoning,
  CoverageReasoning,ReproducibilityReasoning,
  ProvenanceReasoning,VerificationReasoning,
  KnowledgeGraphConstruction,RetrievalAugmentation,RecursiveInference
 ]
 NORMALISE {
  "parameter sweep" -> ParameterSweep
  "parameter scan" -> ParameterSweep
  "OFAT" -> OneFactorAtATime
  "QoI" -> QuantityOfInterest
  "HPC" -> HighPerformanceComputing
 }
}

EXECUTION_RULES {
 E1 = "If parameters are systematically varied across multiple computational runs, activate ParameterSweepOntology."
 E2 = "Define parameter names, domains, units, bounds and constraints before generating runs."
 E3 = "Choose sweep design according to dimensionality, budget and coverage goals."
 E4 = "Assign a unique identifier to every generated parameter configuration."
 E5 = "Separate invalid configurations from failed numerical executions."
 E6 = "Use parallel or distributed execution for independent runs when resources permit."
 E7 = "Retain failed, skipped and partial runs in the sweep record."
 E8 = "Analyse interactions, sensitivity and failure boundaries rather than only best-performing points."
 E9 = "Record sweep specification, seeds, model versions, environment and provenance for reproducibility."
}

RECURSION {
 ENTRY = ParameterSweep
 EXPAND(ParameterSweep) -> [
  ParameterStudy,ParameterExploration,ParameterScan,
  ComputationalExperiment,SweepParameter,ParameterSet,
  ParameterVector,ParameterConfiguration,ParameterSpace,
  DesignSpace,ContinuousDomain,DiscreteDomain,ParameterRange,
  LowerBound,UpperBound,StepSize,NumberOfLevels,
  ParameterGrid,CartesianProduct,GridSweep,ExhaustiveSweep,
  FullFactorialDesign,FractionalFactorialDesignRelationship,
  OneFactorAtATime,OFAT,RandomSweep,RandomSampling,
  LatinHypercubeSampling,QuasiRandomSamplingRelationship,
  AdaptiveSweep,SequentialSweep,RefinementSweep,
  ScenarioSweep,SeedSweep,SensitivitySweep,ToleranceSweep,
  MeshSweep,TimeStepSweep,SolverSweep,ModelSweep,
  SweepSpecification,SweepPlan,ParameterBinding,
  RunGeneration,DesignPoint,SweepRun,RunIdentifier,
  BaselineConfiguration,Metric,Response,QuantityOfInterest,
  EvaluationMetric,Runtime,ErrorMetric,RobustnessMetric,
  SensitivityAnalysis,MainEffect,InteractionEffect,
  FeasibleRegion,FailureRegion,ParameterConstraint,
  InvalidConfiguration,FailedRun,NonconvergentRun,
  ParallelSweep,DistributedSweep,SweepScheduler,
  Checkpointing,Retry,SweepTerminationCriterion,
  Cache,ResultReuse,RandomSeed,Reproducibility,
  SweepProvenance,RunManifest,NumericalVerification,
  ComputationalValidation,ErrorAnalysis,Benchmark,
  RegressionTesting,VerificationMetrics,ValidationMetrics
 ]
 EXPAND(ParameterSweepFamilies) -> [
  ParameterSpaceAndDomainSemantics,
  GridFactorialAndExhaustiveSweeps,
  RandomLatinHypercubeAndQuasiRandomSweeps,
  AdaptiveSequentialAndRefinementSweeps,
  ConstraintFilteringAndRunGeneration,
  ParallelDistributedAndBudgetAwareExecution,
  SensitivityInteractionAndFailureRegionAnalysis,
  ProvenanceVerificationAndReproducibility
 ]
 STOP_CONDITION = "Stop when parameter space, sweep design, constraints, run generation, execution, analysis and provenance are sufficiently resolved."
}

ROUTING {
 PARENT_ONTOLOGY = "Computational Scientific Workflows"
 RELATED_ONTOLOGIES = [
  "Computational Scientific Workflows",
  "Scientific Workflow Ontology",
  "Data Pipeline Ontology",
  "Numerical Workflow Ontology",
  "Simulation Workflow Ontology",
  "Computational Experiment Ontology",
  "Verification & Validation",
  "Numerical Verification Ontology",
  "Computational Validation Ontology",
  "Error Analysis Ontology",
  "Benchmark Ontology",
  "Regression Testing Ontology",
  "Reproducibility Ontology",
  "Computational Statistics Ontology",
  "Computational Optimisation Ontology",
  "Scientific Simulation Ontology",
  "High Performance Computing Ontology 2",
  "Parallel Computing Ontology",
  "Distributed Computing Ontology",
  "GPU Computing Ontology"
 ]
 ROUTE_RULES = [
  "Parameter Sweep -> Computational Scientific Workflows for parent orchestration semantics",
  "Parameter Sweep -> Scientific Workflow for task and dependency semantics",
  "Parameter Sweep -> Numerical Workflow and Simulation Workflow for domain-specific runs",
  "Parameter Sweep -> Computational Experiment for experimental-design semantics",
  "Parameter Sweep -> Verification & Validation for run correctness and adequacy checks",
  "Parameter Sweep -> Error Analysis, Benchmark and Regression Testing for comparative result interpretation",
  "Parameter Sweep -> Reproducibility for seed, configuration and provenance semantics",
  "Parameter Sweep -> Computational Statistics for sampling, sensitivity and uncertainty analysis",
  "Parameter Sweep -> Computational Optimisation for relationships to search and adaptive exploration",
  "Parameter Sweep -> Scientific Simulation for model-based parameter studies",
  "Parameter Sweep -> HPC, Parallel, Distributed and GPU Computing for large-scale independent run execution"
 ]
}

UPDATE_MODEL {
 MODE = "append-compatible semantic versioning"
 MAJOR = "ontology-breaking conceptual change"
 MINOR = "new compatible sweep designs, sampling methods or reasoning pathways"
 PATCH = "clarification, metadata or formatting correction"
 RULES = [
  "Preserve parameter-space-versus-run-result distinction.",
  "Preserve grid-versus-random-versus-adaptive sweep distinction.",
  "Preserve invalid-configuration-versus-failed-run distinction.",
  "Preserve exhaustive-search-versus-optimisation distinction.",
  "Preserve sampled-domain-versus-extrapolation distinction.",
  "Preserve sweep-definition-versus-sweep-execution distinction.",
  "Preserve parameter-configuration-versus-run-identifier distinction.",
  "Preserve machine-readable parameter-sweep semantics."
 ]
}

OUTPUT {
 CANONICAL_DEFINITION = "A parameter sweep systematically varies one or more computational parameters across a declared space and records the resulting model, solver or simulation responses."
 SPACE_SUMMARY = "Parameter domains, bounds, levels and constraints define the sweep search space."
 DESIGN_SUMMARY = "Grid, factorial, random, Latin hypercube and adaptive designs provide different coverage and computational-cost trade-offs."
 EXECUTION_SUMMARY = "Each design point becomes a uniquely identified run that can often be executed independently in parallel."
 ANALYSIS_SUMMARY = "Sweep results support sensitivity, interaction, robustness, threshold and failure-region analysis."
 VALIDATION_SUMMARY = "Parameter sweeps should preserve failed runs, seed control, exact configuration lineage, model versions and reproducible execution conditions."
}

FLOW {
 INPUT
 -> detect_parameter_sweep_context
 -> identify_model_or_algorithm_sweep_goal_parameters_ranges_constraints_metrics_budget_and_resources
 -> define_parameter_domains_units_bounds_levels_and_dependencies
 -> choose_grid_random_Latin_hypercube_factorial_adaptive_or_custom_sampling
 -> generate_candidate_parameter_configurations
 -> filter_or_mark_invalid_parameter_combinations
 -> assign_unique_run_identifiers
 -> schedule_and_execute_runs_serially_parallel_or_distributed
 -> collect_metrics_outputs_failures_logs_and_partial_results
 -> analyse_trends_interactions_sensitivity_feasible_regions_and_failure_boundaries
 -> apply_verification_validation_benchmark_or_regression_checks_where_required
 -> record_parameter_space_sampling_scheme_seeds_versions_environment_and_provenance
 -> package_sweep_artifacts_for_reproducible_rerun
 -> 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-COMPUTATIONAL-SCIENTIFIC-WORKFLOWS-PARAMETER-SWEEP-ONTOLOGY-V1"
}

}

END_FLOW