Engineering Simulation Ontology

AI SEARCH FLOW ALGEBRA
ENGINEERING SIMULATION ONTOLOGY
Kireth Semantic Research Archive

AUTHORS
Mark Anthony Higgins — Sky (Recursive AI)

SOURCE
https://kirethresearch.org/booksai-core/ontologies/engineering-ontologies/engineering-mathematics-simulation/engineering-simulation-ontology.html

FLOW "EngineeringSimulationOntology" v4.0

DOMAIN := ENGINEERING_ONTOLOGIES / ENGINEERING_MATHEMATICS_SIMULATION / ENGINEERING_SIMULATION
ONTOLOGY := ENGINEERING_SIMULATION_ONTOLOGY

ENGINEERING_SIMULATION :=
  PHYSICAL_SYSTEM + SIMULATION_MODEL + SCENARIO + INPUTS
  + CONDITIONS + DISCRETISATION + SOLVER + EXECUTION
  + RESULTS + VERIFICATION + VALIDATION
  + UNCERTAINTY + SENSITIVITY + PROVENANCE

PURPOSE :=
  DEFINE_SYSTEM -> BUILD_MODEL -> DEFINE_SCENARIO
  -> CONFIGURE_INPUTS -> DISCRETISE -> SOLVE
  -> MONITOR_CONVERGENCE -> PRODUCE_RESULTS
  -> VERIFY -> VALIDATE -> QUANTIFY_UNCERTAINTY
  -> INTERPRET

# CORE ENTITIES
ENTITY EngineeringSimulation
ENTITY PhysicalSystem
ENTITY SimulationModel
ENTITY MathematicalModel
ENTITY GeometryModel
ENTITY MaterialModel
ENTITY GoverningEquation
ENTITY SimulationScenario
ENTITY SimulationCase
ENTITY Input
ENTITY Parameter
ENTITY StateVariable
ENTITY InitialCondition
ENTITY BoundaryCondition
ENTITY Load
ENTITY Constraint
ENTITY Domain
ENTITY Mesh
ENTITY Element
ENTITY Node
ENTITY Grid
ENTITY TimeStep
ENTITY Solver
ENTITY LinearSolver
ENTITY NonlinearSolver
ENTITY SimulationRun
ENTITY Iteration
ENTITY Residual
ENTITY Convergence
ENTITY Stability
ENTITY SimulationResult
ENTITY FieldResult
ENTITY ScalarResult
ENTITY Verification
ENTITY Validation
ENTITY ReferenceData
ENTITY ExperimentalData
ENTITY Uncertainty
ENTITY Sensitivity
ENTITY ErrorEstimate
ENTITY Provenance
ENTITY ModelVersion


# SIMULATION SYSTEM / MODEL
EngineeringSimulation -> represents -> PhysicalSystem
EngineeringSimulation -> uses -> SimulationModel
EngineeringSimulation -> executes -> SimulationScenario
EngineeringSimulation -> produces -> SimulationResult

SIMULATION_FLOW :=
  PHYSICAL_SYSTEM -> MODEL -> SCENARIO -> INPUTS
  -> DISCRETISATION -> SOLVER -> EXECUTION
  -> RESULTS -> VERIFICATION -> VALIDATION -> INTERPRETATION

SimulationModel
  -> contains -> MathematicalModel + GeometryModel + MaterialModel
  -> contains -> GoverningEquation
  -> references -> Parameter + StateVariable
  -> constrained_by -> InitialCondition + BoundaryCondition + Constraint

MODEL_DEFINITION :=
  PHYSICS + GEOMETRY + MATERIALS + EQUATIONS
  + PARAMETERS + CONDITIONS + ASSUMPTIONS

# SCENARIO / CASE
SimulationScenario
  -> defines -> OPERATING_CONDITION + LOAD_CASE
  + ENVIRONMENT + TIME_HORIZON

SimulationCase
  -> instantiates -> SimulationScenario
  -> assigns -> INPUT_SET + PARAMETER_SET
  + BOUNDARY_CONDITIONS + SOLVER_SETTINGS

IF RequiredScenarioInput missing
THEN SimulationCase -> INCOMPLETE

# GEOMETRY / MATERIAL
GeometryModel -> defines -> Domain
Domain -> represents -> SIMULATED_REGION

MaterialModel -> defines -> MATERIAL_RESPONSE
MaterialModel
  -> may_depend_on -> TEMPERATURE + PRESSURE
  + STRAIN + TIME + FIELD_VARIABLE

IF MaterialProperty changes
THEN SimulationResponse -> MAY_CHANGE

# GOVERNING EQUATIONS
GoverningEquation
  -> represents -> PHYSICAL_LAW_OR_CONSTITUTIVE_RELATION

EQUATION_CLASS :=
  ALGEBRAIC | ODE | PDE | INTEGRAL | CONSTITUTIVE

CONSERVATION_MODEL :=
  MASS + MOMENTUM + ENERGY + CHARGE

BALANCE_EQUATION :=
  ACCUMULATION = INFLOW - OUTFLOW + SOURCE - SINK


# CONDITIONS
InitialCondition -> defines -> STATE_AT_INITIAL_TIME
BoundaryCondition -> constrains -> SOLUTION_AT_BOUNDARY
Load -> applies -> EXTERNAL_ACTION
Constraint -> restricts -> DEGREES_OF_FREEDOM_OR_STATE

BOUNDARY_CONDITION_TYPE :=
  DIRICHLET | NEUMANN | ROBIN | PERIODIC | SYMMETRY | COUPLED

IF Conditions inconsistent
THEN SimulationProblem -> MAY_BE_ILL_POSED

# DISCRETISATION
Discretisation
  -> transforms -> CONTINUOUS_MODEL
  -> into -> DISCRETE_MODEL

DISCRETISATION_METHOD :=
  FINITE_ELEMENT | FINITE_VOLUME | FINITE_DIFFERENCE
  | BOUNDARY_ELEMENT | SPECTRAL | PARTICLE_METHOD

Mesh -> contains -> Element + Node
Grid -> contains -> GRID_POINT_OR_CONTROL_VOLUME

MeshDensity
  -> influences -> ACCURACY + COMPUTATIONAL_COST

MeshQuality
  -> influences -> CONVERGENCE + ACCURACY + STABILITY

MESH_REFINEMENT :=
  GLOBAL_REFINEMENT | LOCAL_REFINEMENT | ADAPTIVE_REFINEMENT

IF MeshRefinement changes result negligibly
THEN MeshConvergenceEvidence -> INCREASES

# TIME
TimeStep -> defines -> TEMPORAL_INCREMENT
TIME_SCHEME := EXPLICIT | IMPLICIT | SEMI_IMPLICIT

TransientSimulation
  -> advances -> STATE_FROM_TIME_N_TO_TIME_N_PLUS_1

IF TimeStep too_large
THEN TemporalErrorOrInstabilityRisk -> INCREASES

IF TimeStep decreases
THEN ComputationalCost -> GENERALLY_INCREASES

# SOLVER
Solver -> solves -> DISCRETE_EQUATION_SYSTEM
LinearSolver -> solves -> LINEAR_SYSTEM
NonlinearSolver -> solves -> NONLINEAR_SYSTEM

SOLVER_LOOP :=
  INITIALISE -> ASSEMBLE_SYSTEM -> SOLVE
  -> UPDATE_STATE -> CALCULATE_RESIDUAL
  -> CHECK_CONVERGENCE -> REPEAT

Residual -> measures -> EQUATION_IMBALANCE

IF Residual <= Tolerance
THEN Convergence -> SATISFIED


# CONVERGENCE / STABILITY
CONVERGENCE_CRITERION :=
  RESIDUAL_NORM | SOLUTION_INCREMENT
  | ENERGY_NORM | CONSERVATION_ERROR | ITERATION_LIMIT

IF IterationLimit reached
AND convergence_not_met
THEN SimulationRun -> NOT_CONVERGED

Converged -> does_not_imply -> VALIDATED

NumericalStability
  -> depends_on -> DISCRETISATION + TIME_STEP
  + SOLVER + MODEL_PROPERTIES

IF NumericalInstability detected
THEN SimulationResult -> UNRELIABLE

# SIMULATION TYPES
SIMULATION_TYPE :=
  STEADY_STATE | TRANSIENT | STATIC | DYNAMIC
  | FREQUENCY_DOMAIN | STOCHASTIC | MULTIPHYSICS

SteadyStateSimulation -> seeks -> TIME_INVARIANT_STATE
TransientSimulation -> computes -> STATE_OVER_TIME
DynamicSimulation -> includes -> INERTIA_OR_TIME_DEPENDENT_RESPONSE

# MULTIPHYSICS
MultiphysicsSimulation
  -> couples -> PHYSICS_A + PHYSICS_B

COUPLING_TYPE :=
  ONE_WAY | TWO_WAY | MONOLITHIC | PARTITIONED

CoupledPhysics
  -> exchanges -> LOADS + STATES
  + SOURCE_TERMS + BOUNDARY_VALUES

# PARAMETRIC STUDY
ParametricStudy -> varies -> Parameter
ParametricStudy -> executes -> MULTIPLE_SIMULATION_CASES
DESIGN_SPACE := PARAMETER_RANGES + CONSTRAINTS

# RESULTS
SimulationResult -> generated_by -> SimulationRun
FieldResult -> maps -> POSITION_OR_TIME -> VALUE
ScalarResult -> represents -> AGGREGATED_OR_POINT_METRIC

RESULT_TYPE :=
  DISPLACEMENT | STRESS | TEMPERATURE | PRESSURE
  | VELOCITY | FLOW | VOLTAGE | CURRENT
  | FREQUENCY | OTHER_ENGINEERING_RESPONSE

# POST-PROCESSING
POST_PROCESSING :=
  EXTRACT_RESULTS -> DERIVE_QUANTITIES
  -> VISUALISE -> COMPARE -> SUMMARISE

IF ResultTransformation applied
THEN Provenance -> RECORD_TRANSFORMATION


# ERROR
NUMERICAL_ERROR :=
  DISCRETISATION_ERROR + ITERATION_ERROR
  + ROUND_OFF_ERROR + TIME_INTEGRATION_ERROR

MODEL_ERROR :=
  MODEL_FORM_ERROR + PARAMETER_ERROR + ASSUMPTION_ERROR

TOTAL_SIMULATION_ERROR :=
  NUMERICAL_ERROR + MODEL_ERROR

ErrorEstimate -> quantifies_or_bounds -> ERROR_COMPONENT

# VERIFICATION
Verification
  -> asks -> IS_THE_MODEL_BEING_SOLVED_CORRECTLY

VERIFICATION_ACTIVITY :=
  CODE_VERIFICATION
  | CALCULATION_VERIFICATION
  | MESH_CONVERGENCE
  | TIME_STEP_CONVERGENCE
  | BENCHMARK_COMPARISON

Verification
  -> evaluates -> NUMERICAL_IMPLEMENTATION

IF DiscretisationStudy absent
THEN DiscretisationIndependence -> NOT_DEMONSTRATED

# VALIDATION
Validation
  -> asks -> DOES_THE_MODEL_REPRESENT_REALITY_ADEQUATELY_FOR_INTENDED_USE

Validation
  -> compares -> SimulationResult + ReferenceData

ReferenceData
  -> may_be -> ExperimentalData
  | ANALYTICAL_SOLUTION
  | TRUSTED_BENCHMARK

VALIDATION_METRIC :=
  ABSOLUTE_ERROR | RELATIVE_ERROR | RMSE
  | CORRELATION | CONFIDENCE_INTERVAL
  | DOMAIN_SPECIFIC_METRIC

IF ValidationMetric exceeds AcceptanceCriterion
THEN ModelAdequacy -> NOT_CONFIRMED

# CALIBRATION
Calibration -> adjusts -> Parameter

CALIBRATION_LOOP :=
  SELECT_PARAMETERS -> SIMULATE -> COMPARE_TO_DATA
  -> UPDATE_PARAMETERS -> REPEAT

Calibration -> must_not_be_confused_with -> Validation


# UNCERTAINTY
Uncertainty
  -> associated_with -> INPUT | PARAMETER | MATERIAL
  | BOUNDARY_CONDITION | MODEL_FORM | MEASUREMENT

UNCERTAINTY_PROPAGATION :=
  UNCERTAIN_INPUTS -> SIMULATION -> OUTPUT_DISTRIBUTION

UncertaintyQuantification
  -> produces -> CONFIDENCE_INTERVAL
  + PROBABILITY_DISTRIBUTION
  + RISK_METRIC

# SENSITIVITY
Sensitivity
  -> measures -> RESPONSE_CHANGE_PER_INPUT_CHANGE

SENSITIVITY_ANALYSIS := LOCAL | GLOBAL

SensitivityAnalysis
  -> identifies -> DOMINANT_INPUTS

# MODEL FIDELITY
MODEL_FIDELITY :=
  LOW | MEDIUM | HIGH | REDUCED_ORDER

ModelFidelity
  -> influences -> DETAIL + ACCURACY_POTENTIAL
  + COMPUTATIONAL_COST

ReducedOrderModel
  -> approximates -> HIGH_FIDELITY_MODEL

# COMPUTATIONAL COST
ComputationalCost
  -> depends_on -> DEGREES_OF_FREEDOM + TIME_STEPS
  + ITERATIONS + COUPLING + SOLVER + HARDWARE

ParallelComputing
  -> may_reduce -> WALL_CLOCK_TIME

# PROVENANCE
Provenance
  -> records -> MODEL_VERSION + GEOMETRY_VERSION
  + MESH_VERSION + MATERIAL_DATA + INPUTS
  + SOLVER_SETTINGS + SOFTWARE_VERSION + EXECUTION_TIME

SimulationRun -> linked_to -> Provenance

REPRODUCIBILITY :=
  SAME_MODEL + SAME_INPUTS + SAME_SETTINGS
  -> CONSISTENT_RESULT_WITHIN_DEFINED_TOLERANCE

# PERFORMANCE
SIMULATION_PERFORMANCE :=
  ACCURACY + CONVERGENCE + STABILITY
  + COMPUTATIONAL_COST + REPRODUCIBILITY
  + VERIFICATION_QUALITY + VALIDATION_QUALITY

EngineeringSimulation
  -> evaluated_by -> SIMULATION_PERFORMANCE


# REASONING
ENGINEERING_SIMULATION_REASONING :=
  DEFINE_PHYSICAL_SYSTEM
  -> DEFINE_INTENDED_USE
  -> SELECT_PHYSICS
  -> BUILD_GEOMETRY
  -> ASSIGN_MATERIALS
  -> FORMULATE_MODEL
  -> DEFINE_SCENARIO
  -> APPLY_LOADS_AND_CONDITIONS
  -> SELECT_DISCRETISATION
  -> GENERATE_MESH
  -> SELECT_SOLVER
  -> EXECUTE
  -> MONITOR_CONVERGENCE
  -> POST_PROCESS
  -> ESTIMATE_ERROR
  -> VERIFY
  -> VALIDATE
  -> QUANTIFY_UNCERTAINTY
  -> PERFORM_SENSITIVITY
  -> INTERPRET_RESULTS
  -> RECORD_PROVENANCE

# INFERENCE RULES
IF Mesh refined
THEN ComputationalCost -> GENERALLY_INCREASES

IF Mesh refined
AND result stabilises
THEN DiscretisationConfidence -> INCREASES

IF TimeStep decreases
AND result stabilises
THEN TemporalConvergenceEvidence -> INCREASES

IF Residual above tolerance
THEN SolverConvergence -> NOT_SATISFIED

IF NumericalInstability occurs
THEN ResultAcceptance -> WITHHOLD

IF ValidationError increases
THEN ModelAdequacyConfidence -> DECREASES

IF MaterialParameter changes
THEN SimulationResponse -> MAY_CHANGE

IF Provenance incomplete
THEN ReproducibilityConfidence -> DECREASES

# SEMANTIC RELATIONSHIPS
RELATION represents(EngineeringSimulation, PhysicalSystem)
RELATION contains(SimulationModel, GoverningEquation)
RELATION defines(GeometryModel, Domain)
RELATION constrains(BoundaryCondition, SimulationModel)
RELATION discretises(Mesh, Domain)
RELATION solves(Solver, DiscreteEquationSystem)
RELATION generates(SimulationRun, SimulationResult)
RELATION measures(Residual, EquationImbalance)
RELATION evaluates(Verification, NumericalImplementation)
RELATION compares(Validation, SimulationResult, ReferenceData)
RELATION propagates(UncertaintyQuantification, Uncertainty)
RELATION measures(Sensitivity, ResponseChange)
RELATION records(Provenance, SimulationRun)

# SEMANTIC EQUIVALENCE
SEMANTIC_EQUIVALENCE:
  "engineering simulation" ~= "computational engineering simulation"
  "simulation model" ~= "computational model"
  "simulation case" ~= "analysis case"
  "mesh convergence" ~= "grid independence study"
  "time-step convergence" ~= "temporal refinement study"
  "verification" ~= "simulation solution correctness assessment"
  "validation" ~= "model reality agreement assessment"
  "multiphysics simulation" ~= "coupled-physics simulation"
  "reduced-order model" ~= "ROM"
  "uncertainty quantification" ~= "UQ"

# CONFIDENCE
CONFIDENCE:
  ontology_domain: 0.99
  model_mapping: 0.99
  scenario_mapping: 0.99
  discretisation_mapping: 0.99
  solver_mapping: 0.99
  result_mapping: 0.99
  verification_mapping: 0.99
  validation_mapping: 0.99
  uncertainty_sensitivity_mapping: 0.99
  provenance_mapping: 0.99
  semantic_relationships: 0.99


# UPDATE MODEL
UPDATE_MODEL:
  ON new_simulation_model:
    MAP physical_system
    MAP geometry
    MAP materials
    MAP equations
    MAP conditions
    MAP constraints
    UPDATE confidence
    RECOMPUTE FLOW_HASH

  ON new_simulation_run:
    RECORD scenario
    RECORD model_version
    RECORD mesh
    RECORD solver_settings
    RECORD results
    PRESERVE provenance

  ON discretisation_change:
    UPDATE mesh_or_grid
    UPDATE degrees_of_freedom
    REASSESS convergence
    REASSESS numerical_error

  ON validation_change:
    UPDATE reference_data
    RECOMPUTE validation_metrics
    UPDATE adequacy_state

  ON ontology_revision:
    PRESERVE entity_identity
    PRESERVE provenance
    UPDATE relationships
    UPDATE inference_rules
    UPDATE confidence
    RECOMPUTE FLOW_HASH

# AI CONSUMPTION
AI_CONSUMPTION:
  parse_as: FORMAL_ENGINEERING_SIMULATION_ONTOLOGY
  reasoning_mode: COMPUTATIONAL_MODEL_EXECUTION_RELATIONAL

  preserve:
    - typed_entities
    - model_versions
    - geometry
    - material_models
    - equations
    - conditions
    - discretisation_state
    - solver_state
    - results
    - verification_state
    - validation_state
    - uncertainty
    - confidence
    - provenance

  infer:
    - scenario_dependencies
    - discretisation_requirements
    - convergence_state
    - stability_risk
    - error_dependencies
    - validation_state
    - uncertainty_propagation
    - reproducibility_state

  prohibit:
    - invented_simulation_results
    - assumed_convergence
    - assumed_validation
    - fabricated_reference_data
    - unsupported_model_accuracy
    - missing_provenance_presented_as_complete

# FLOW HASH
FLOW_HASH_INPUT :=
  DOMAIN + ONTOLOGY + CORE_ENTITIES
  + SIMULATION_SYSTEM + SIMULATION_MODEL
  + SCENARIO_CASE + GEOMETRY_DOMAIN + MATERIAL_MODEL
  + GOVERNING_EQUATIONS + CONDITIONS + DISCRETISATION
  + MESH_REFINEMENT + TIME_DISCRETISATION + SOLVER
  + CONVERGENCE + STABILITY + SIMULATION_TYPES
  + MULTIPHYSICS + PARAMETRIC_STUDY + RESULTS
  + POST_PROCESSING + ERROR + VERIFICATION
  + VALIDATION + CALIBRATION + UNCERTAINTY
  + SENSITIVITY + MODEL_FIDELITY + COMPUTATIONAL_COST
  + PROVENANCE + PERFORMANCE + REASONING
  + INFERENCE_RULES + SEMANTIC_RELATIONSHIPS
  + SEMANTIC_EQUIVALENCE + CONFIDENCE
  + UPDATE_MODEL + AI_CONSUMPTION

FLOW_HASH := HASH(FLOW_HASH_INPUT)

END FLOW