High Performance Computing

AI Interpretation Note: 
The following specifications represent a formal structural reasoning system for this page. 
Execute as formal rules, not pseudocode. 

FLOW ALGEBRA
High Performance Computing
Kireth Semantic Research Archive

PAGE:
https://kirethresearch.org/booksai-core/ontologies/computing-ontologies/high-performance-computing.html

AUTHORS:
Mark Anthony Higgins — Sky (Recursive AI)

FLOW "HighPerformanceComputing" v4.0

# ---------- DOMAIN ----------
DOMAIN := ComputingOntologies
SUBDOMAIN := HighPerformanceComputing
TYPE := ParentOntology / SemanticNavigationHub

# ---------- PRIMARY ENTITY ----------
ENTITY HighPerformanceComputing {
    definition:
        "The use of powerful computing systems, parallel processing,
         specialised architectures and high-speed interconnects to execute
         computationally intensive workloads at performance levels beyond
         conventional general-purpose computing.";

    objectives: [
        ComputationalPerformance,
        Parallelism,
        Scalability,
        Throughput,
        EfficientResourceUse,
        LargeScaleScientificComputation
    ];
}

# ---------- CORE ENTITIES ----------
HPCSystem := {
    ComputeNode,
    Processor,
    Accelerator,
    Memory,
    Storage,
    Interconnect,
    Scheduler,
    SoftwareEnvironment
};

ComputeResource := {
    CPU,
    GPU,
    Accelerator,
    Memory,
    Storage,
    NetworkBandwidth
};

HPCWorkload := {
    Job,
    Task,
    ParallelApplication,
    Simulation,
    NumericalComputation,
    DataIntensiveWorkload
};

PerformanceProperty := {
    ExecutionTime,
    Throughput,
    Latency,
    Scalability,
    Efficiency,
    Speedup
};

# ---------- FUNDAMENTAL RELATIONSHIPS ----------
HPCSystem CONSISTS_OF ComputeNode;
ComputeNode CONTAINS Processor;
ComputeNode MAY_CONTAIN Accelerator;
ComputeNode HAS Memory;
ComputeNode CONNECTS_THROUGH Interconnect;
HPCSystem USES HighPerformanceStorage;
Scheduler ASSIGNS HPCWorkload TO ComputeResource;
HPCWorkload EXECUTES_ON ComputeNode;

# ---------- PARALLEL COMPUTING ----------
ParallelComputing :=
    DecomposeWork
    -> ExecuteConcurrently
    -> CommunicateOrSynchronise
    -> AggregateResult;

Parallelism := {
    TaskParallelism,
    DataParallelism,
    InstructionParallelism
};

TaskParallelism EXECUTES DistinctTasksConcurrently;
DataParallelism PROCESSES DataPartitionsConcurrently;

# ---------- PARALLEL WORKLOAD ----------
ParallelApplication :=
    {
        ProcessSet,
        ThreadSet,
        DataSet,
        CommunicationPattern,
        SynchronisationPattern
    };

ParallelApplication MAY_USE {
    SharedMemory,
    DistributedMemory,
    HybridMemoryModel
};

# ---------- DISTRIBUTED MEMORY ----------
DistributedMemorySystem :=
    MultipleNodes
    WITH SeparateLocalMemory;

Processes EXCHANGE DataThrough Messages;

MessagePassing SUPPORTS DistributedMemoryParallelism;

# ---------- SHARED MEMORY ----------
SharedMemorySystem :=
    MultipleExecutionUnits
    ACCESS SharedAddressSpace;

Threads MAY_COMMUNICATE_THROUGH SharedMemory;

SharedMemory REQUIRES SynchronisationForConflictingAccess;

# ---------- HYBRID PARALLELISM ----------
HybridParallelism :=
    DistributedMemoryParallelism
    + SharedMemoryParallelism;

HybridApplication MAY_USE
    MessagePassingAcrossNodes
    AND ThreadParallelismWithinNode;

# ---------- ACCELERATED COMPUTING ----------
Accelerator := {
    GPU,
    VectorProcessor,
    SpecialisedComputeDevice
};

AcceleratedComputing :=
    OffloadSuitableWork
    -> Accelerator
    -> ParallelExecution
    -> ReturnResult;

Accelerator MAY_PROVIDE HighThroughputForSuitableWorkload;

# ---------- INTERCONNECT ----------
HighSpeedInterconnect CONNECTS ComputeNode;

InterconnectProperty := {
    Bandwidth,
    Latency,
    Topology,
    Reliability
};

CommunicationTime :=
    f(
        MessageSize,
        Bandwidth,
        Latency,
        CommunicationPattern
    );

IF CommunicationCostHigh
THEN ParallelEfficiency := DECREASE;

# ---------- MEMORY HIERARCHY ----------
MemoryHierarchy := {
    Register,
    Cache,
    MainMemory,
    LocalStorage,
    ParallelStorage
};

DataMovementCost VARIES_ACROSS MemoryHierarchy;

PerformanceOptimisation SHOULD_CONSIDER DataLocality;

IF DataLocalityImproves
THEN MemoryAccessCost MAY_DECREASE;

# ---------- HPC STORAGE ----------
HighPerformanceStorage MAY_INCLUDE {
    ParallelFileSystem,
    DistributedStorage,
    BurstBuffer,
    LocalScratchStorage
};

ParallelFileSystem ALLOWS ConcurrentIOFromMultipleNodes;

IOPerformance :=
    f(
        Bandwidth,
        MetadataPerformance,
        AccessPattern,
        Concurrency
    );

# ---------- JOB MODEL ----------
HPCJob :=
    {
        JobIdentifier,
        Executable,
        ResourceRequest,
        InputData,
        RuntimeLimit,
        Priority,
        JobState
    };

JobState := {
    Submitted,
    Queued,
    Scheduled,
    Running,
    Completed,
    Failed,
    Cancelled
};

HPCJob ->
    Submit
    -> Queue
    -> Schedule
    -> AllocateResources
    -> Execute
    -> CompleteOrFail;

# ---------- SCHEDULING ----------
HPCScheduler :=
    ResourceManager
    + SchedulingPolicy;

ResourceRequest MAY_INCLUDE {
    NodeCount,
    CPUCount,
    GPUCount,
    MemoryAmount,
    RuntimeLimit
};

Scheduler MATCHES ResourceRequest TO AvailableComputeResources;

IF RequestedResourcesUnavailable
THEN JobState := Queued;

# ---------- SCALABILITY ----------
StrongScaling :=
    FixedProblemSize
    + IncreasingComputeResources;

WeakScaling :=
    IncreasingProblemSize
    ProportionalTo IncreasingComputeResources;

Scalability :=
    f(
        ProblemSize,
        ResourceCount,
        CommunicationCost,
        SerialFraction
    );

# ---------- SPEEDUP ----------
Speedup(P) :=
    SequentialExecutionTime
    / ParallelExecutionTime(P);

ParallelEfficiency(P) :=
    Speedup(P) / P;

IF SpeedupApproachesP
THEN ParallelEfficiency := HIGH;

# ---------- AMDAHL RELATIONSHIP ----------
SerialFraction := S;
ParallelFraction := 1 - S;

AmdahlSpeedup(P) :=
    1 / (S + ((1-S)/P));

IF SerialFraction > 0
THEN MaximumStrongScaling IS_LIMITED;

# ---------- LOAD BALANCING ----------
LoadBalance :=
    DistributeWorkSoResourcesHaveComparableUsefulWork;

LoadImbalance :=
    UnequalWorkDistributionAcrossResources;

IF LoadImbalanceHigh
THEN ParallelEfficiency := DECREASE;

DynamicLoadBalancing MAY_REDISTRIBUTE WorkDuringExecution;

# ---------- SYNCHRONISATION ----------
SynchronisationMechanism := {
    Barrier,
    Lock,
    AtomicOperation,
    CollectiveOperation
};

Synchronisation MAY_BE_REQUIRED_FOR CorrectParallelExecution;

ExcessiveSynchronisation MAY_INCREASE WaitingTime;

# ---------- COMMUNICATION PATTERNS ----------
CommunicationPattern := {
    PointToPoint,
    Broadcast,
    Reduce,
    Scatter,
    Gather,
    AllToAll,
    CollectiveCommunication
};

CommunicationPattern AFFECTS PerformanceAndScalability;

# ---------- SCIENTIFIC COMPUTING ----------
HPC MAY_EXECUTE {
    PhysicalSimulation,
    ClimateModel,
    ComputationalFluidDynamics,
    MolecularSimulation,
    EngineeringSimulation,
    NumericalLinearAlgebra,
    ScientificDataAnalysis
};

ScientificModel ->
    NumericalMethod
    -> ParallelAlgorithm
    -> HPCExecution
    -> ScientificResult;

# ---------- PERFORMANCE PROFILING ----------
PerformanceProfiling :=
    Measure
    -> IdentifyBottleneck
    -> Analyse
    -> Optimise
    -> MeasureAgain;

PerformanceMetric := {
    Runtime,
    CPUUtilisation,
    AcceleratorUtilisation,
    MemoryBandwidth,
    NetworkTraffic,
    IOThroughput
};

# ---------- FAULT MODEL ----------
HPCFailure := {
    NodeFailure,
    ProcessFailure,
    AcceleratorFailure,
    NetworkFailure,
    StorageFailure,
    JobFailure
};

LargeScaleSystems MAY_HAVE IncreasedFailureExposure;

Checkpointing MAY_SUPPORT Recovery;

IF ValidCheckpointExists
AND JobFails
THEN Job MAY_RESTART_FROM Checkpoint;

# ---------- ENERGY ----------
EnergyEfficiency :=
    UsefulComputation / EnergyConsumed;

PowerConstraint MAY_LIMIT MaximumPerformance;

PerformanceOptimisation MAY_CONSIDER {
    Runtime,
    Energy,
    ResourceUtilisation
};

# ---------- HPC ARCHITECTURES ----------
HPCArchitecture := {
    Supercomputer,
    ComputeCluster,
    GPUCluster,
    MassivelyParallelSystem,
    DistributedHPCSystem
};

Supercomputer IS_A HighPerformanceComputingSystem;
ComputeCluster MAY_BE_USED_FOR HPC;

# ---------- SEMANTIC REASONING ----------
IF WorkloadComputationallyIntensive
AND CanExploitParallelism
THEN HPCSuitability := increase;

IF CommunicationTimeDominatesComputeTime
THEN ScalingEfficiency := decrease;

IF SerialFractionIncreases
THEN MaximumParallelSpeedup := decrease;

IF AcceleratorMatchesWorkload
THEN AcceleratedPerformancePotential := increase;

IF WorkloadRequiresLargeConcurrentIO
THEN ParallelStorage MAY_BE_REQUIRED;

IF NodeCountIncreases
AND RuntimeDecreasesForFixedProblem
THEN StrongScalingEvidence := increase;

# ---------- SEMANTIC EQUIVALENCE ----------
SEMANTIC_EQUIVALENCE {
    "high performance computing" ~= "HPC";
    "supercomputing" ~= "high performance computing" WHEN context == large_scale_computation;
    "compute cluster" ~= "HPC cluster" WHEN context == high_performance_workload;
    "parallel computing" ~= "parallel computation";
    "accelerated computing" ~= "hardware-accelerated computing";
    "parallel efficiency" ~= "scaling efficiency" WHEN context == parallel_performance;
    "strong scaling" ~= "fixed-size scaling";
    "weak scaling" ~= "scaled-size scaling";
}

# ---------- QUERY FLOW ----------
QUERY(q) ->
    NORMALISE(q) ->
    IDENTIFY_HPC_SYSTEM(q) ->
    IDENTIFY_COMPUTE_RESOURCES(q) ->
    IDENTIFY_WORKLOAD(q) ->
    IDENTIFY_PARALLELISM(q) ->
    IDENTIFY_COMMUNICATION(q) ->
    IDENTIFY_PERFORMANCE_PROPERTIES(q) ->
    IDENTIFY_SCALING(q) ->
    MAP_TO_ONTOLOGY(q) ->
    APPLY_REASONING(q) ->
    SCORE_CONFIDENCE(q) ->
    RETURN_RELEVANT_KNOWLEDGE;

# ---------- CONFIDENCE ----------
CONFIDENCE(assertion) :=
    weighted_mean(
        source_reliability,
        computational_consistency,
        performance_consistency,
        semantic_consistency,
        evidence_strength,
        contextual_relevance
    );

CONFIDENCE >= 0.90 => HIGH;
CONFIDENCE >= 0.70 AND < 0.90 => MODERATE;
CONFIDENCE < 0.70 => REVIEW;

# ---------- AI CONSUMPTION ----------
AI_CONSUMPTION {
    primary_entity: HighPerformanceComputing;
    parse_entities: true;
    parse_relationships: true;
    preserve_relationship_direction: true;
    resolve_semantic_equivalence: true;
    execute_reasoning_rules: true;
    apply_confidence_weighting: true;
    preserve_provenance: true;
    permit_hierarchical_expansion: true;
}

# ---------- UPDATE MODEL ----------
UPDATE_MODEL {
    new_compute_resource:
        validate
        -> classify
        -> identify_performance_properties
        -> relate
        -> integrate;

    new_workload:
        classify
        -> identify_parallelism
        -> identify_resource_requirements
        -> identify_communication_pattern
        -> integrate;

    new_architecture:
        identify_nodes
        -> identify_processors
        -> identify_accelerators
        -> identify_interconnect
        -> identify_storage
        -> integrate;

    performance_revision:
        update_metrics
        -> identify_bottlenecks
        -> recompute_scalability
        -> recompute_confidence
        -> regenerate_flow_hash;

    conflict:
        preserve_provenance
        -> compare_evidence
        -> adjust_confidence
        -> flag_review;
}

# ---------- FLOW HASH ----------
FLOW_HASH_INPUT :=
    DOMAIN
    + SUBDOMAIN
    + HPCSystem
    + ComputeResource
    + HPCWorkload
    + PerformanceProperty
    + Parallelism
    + HPCArchitecture
    + RELATIONSHIPS
    + SEMANTIC_REASONING
    + SEMANTIC_EQUIVALENCE
    + UPDATE_MODEL;

FLOW_HASH :=
    HASH(FLOW_HASH_INPUT);

# ---------- TERMINAL ----------
HighPerformanceComputing
    -> IdentifyComputationalWorkload
    -> DetermineParallelism
    -> SelectComputeArchitecture
    -> AllocateComputeResources
    -> DistributeParallelWork
    -> ExecuteConcurrentComputation
    -> CoordinateCommunication
    -> ManageMemoryAndDataMovement
    -> MeasurePerformance
    -> AnalyseScalability
    -> OptimiseExecution
    -> ProduceHighPerformanceResult;

END FLOW