GPU_CROSS_DOMAIN_METHODS

GPU-Beschleunigte Analysemethoden für ThemisDB

Stand: 5. Dezember 2025
Version: 1.0.0
Kategorie: Analysis

---

Cross-Domain Pattern Recognition & Search Optimization

Datum: 20. November 2025
Status: Konzept & Machbarkeitsanalyse
Scope: Finanz, Technik, Wirtschaft → Datenbank-Optimierung

---

Executive Summary

Frage: Welche Analysemethoden aus Finanz, Technik und Wirtschaft können GPU-gestützte Suche und Mustererkennung in ThemisDB verbessern?

Antwort: ✅ JA - Viele hochrelevante Methoden verfügbar!

Top 10 Methoden mit höchstem ROI:

Methode	Branche	GPU-Speedup	ThemisDB Use Case	Priorität
Time Series Analysis	Finanz	50-100x	Log-Analyse, Monitoring, Trends	P0
Anomaly Detection	Finanz/Security	20-50x	Fraud Detection, Security	P0
Signal Processing (FFT)	Technik	100-500x	Pattern Matching, Similarity	P1
Monte Carlo Simulation	Finanz	100-1000x	Risk Analysis, Forecasting	P1
Spectral Clustering	ML/Wirtschaft	10-50x	Community Detection	P1
Wavelet Transform	Technik	50-200x	Multi-Scale Pattern Search	P2
Dynamic Time Warping	Wirtschaft	20-100x	Sequence Similarity	P2
Kalman Filter	Technik	50-150x	State Estimation, Prediction	P2
Hidden Markov Models	Finanz	30-80x	Sequence Prediction	P3
Tensor Decomposition	ML	50-200x	Multi-Dimensional Analysis	P3

---

1. FINANZ-METHODEN

1.1 Time Series Analysis (ARIMA, GARCH)

Was ist es?

• AutoRegressive Integrated Moving Average
• GARCH (Generalized AutoRegressive Conditional Heteroskedasticity)
• Vorhersage von Zeitreihen mit Saisonalität und Trends

GPU-Beschleunigung:

class GPUTimeSeriesAnalyzer {
public:
    // ARIMA Model auf GPU
    struct ARIMAModel {
        int p, d, q;  // AR, Integration, MA orders
        std::vector<double> coefficients;
    };
    
    // Batch ARIMA fitting für viele Zeitreihen parallel
    std::vector<ARIMAModel> fitARIMA_GPU(
        const std::vector<std::vector<double>>& timeSeries,
        int p, int d, int q
    );
    
    // Forecast nächste N Werte
    std::vector<std::vector<double>> forecast_GPU(
        const std::vector<ARIMAModel>& models,
        int horizon
    );
};

ThemisDB Use Cases:

• Log Analytics: Server-Logs, API-Zugriffe vorhersagen
• Usage Patterns: Datenbank-Last-Vorhersage
• Monitoring: Anomalien in Metriken erkennen
• Business Analytics: Sales Forecasting aus DB-Daten

Beispiel:

-- AQL mit Time Series Analysis
FOR metric IN server_metrics
  LET forecast = GPU_ARIMA_FORECAST(
    metric.cpu_usage,
    horizon: 24,  // 24 hours ahead
    confidence: 0.95
  )
  FILTER forecast.prediction > 0.8  // High CPU predicted
  RETURN {
    server: metric.server_id,
    current: metric.cpu_usage[-1],
    predicted: forecast.prediction,
    alert: forecast.prediction > 0.8
  }

Performance:

• CPU: 100 Zeitreihen/Sekunde
• GPU: 10,000+ Zeitreihen/Sekunde
• Speedup: 100x

---

1.2 Anomaly Detection (Isolation Forest, DBSCAN)

Was ist es?

• Erkennung von Ausreißern in hochdimensionalen Daten
• Fraud Detection in Finanztransaktionen
• Cybersecurity: Anomale Zugriffsmuster

GPU-Implementierung:

class GPUAnomalyDetector {
public:
    // Isolation Forest auf GPU
    struct IsolationForest {
        int numTrees;
        int maxDepth;
        std::vector<void*> trees;  // GPU tree structures
    };
    
    // Trainiere Isolation Forest
    IsolationForest train_GPU(
        const float* data,
        size_t numSamples,
        size_t numFeatures,
        int numTrees = 100
    );
    
    // Batch anomaly scoring
    std::vector<double> detectAnomalies_GPU(
        const IsolationForest& forest,
        const float* data,
        size_t numSamples
    );
    
    // DBSCAN Clustering für Anomaly Detection
    std::vector<int> dbscan_GPU(
        const float* data,
        size_t numSamples,
        size_t numFeatures,
        double eps,
        int minPoints
    );
};

ThemisDB Use Cases:

• Fraud Detection: Verdächtige Transaktionen in Echtzeit
• Security: Anomale Login-Patterns
• Data Quality: Outlier Detection in Datasets
• System Monitoring: Anomale Server-Metriken

Beispiel:

-- Real-time Fraud Detection
FOR transaction IN transactions
  COLLECT batch = BATCH(transaction, 1000)
  LET anomalyScores = GPU_ISOLATION_FOREST(
    ATTRIBUTES(batch, ["amount", "location", "time", "merchant"])
  )
  FOR i IN 0..LENGTH(batch)-1
    FILTER anomalyScores[i] > 0.7  // High anomaly score
    RETURN {
      transaction: batch[i],
      anomalyScore: anomalyScores[i],
      flagged: true
    }

Performance:

• CPU: 1,000 Samples/Sekunde
• GPU: 50,000+ Samples/Sekunde
• Speedup: 50x

---

1.3 Monte Carlo Simulation

Was ist es?

• Probabilistische Simulation für Risikoanalyse
• Value at Risk (VaR) Berechnung
• Portfolio Optimization

GPU-Implementierung:

class GPUMonteCarloSimulator {
public:
    // Monte Carlo VaR Berechnung
    struct VaRResult {
        double var_95;
        double var_99;
        double expectedLoss;
        std::vector<double> scenarios;
    };
    
    VaRResult calculateVaR_GPU(
        const std::vector<double>& returns,
        const std::vector<double>& weights,
        int numSimulations = 1000000
    );
    
    // Path simulation (z.B. für Option Pricing)
    std::vector<std::vector<double>> simulatePaths_GPU(
        double S0,      // Initial value
        double mu,      // Drift
        double sigma,   // Volatility
        int numPaths,
        int numSteps
    );
};

ThemisDB Use Cases:

• Risk Analytics: Portfolio Risk Berechnung
• What-If Analysis: Business Scenario Simulation
• Capacity Planning: Server-Load Simulation
• A/B Testing: Statistical Significance Testing

Performance:

• CPU: 10,000 Simulations/Sekunde
• GPU: 10,000,000+ Simulations/Sekunde
• Speedup: 1000x (massiv parallel)

---

2. TECHNIK-METHODEN

2.1 Fast Fourier Transform (FFT)

Was ist es?

• Frequenz-Analyse von Signalen
• Pattern Matching im Frequenz-Domain
• Periodizitätserkennung

GPU-Implementierung:

class GPUSignalProcessor {
public:
    // Batch FFT für viele Zeitreihen
    std::vector<std::vector<std::complex<double>>> batchFFT_GPU(
        const std::vector<std::vector<double>>& signals
    );
    
    // Convolution via FFT (für Pattern Matching)
    std::vector<double> convolution_GPU(
        const std::vector<double>& signal,
        const std::vector<double>& pattern
    );
    
    // Spectral similarity
    double spectralSimilarity_GPU(
        const std::vector<double>& signal1,
        const std::vector<double>& signal2
    );
};

ThemisDB Use Cases:

• Pattern Matching: Ähnliche Zeitreihen finden (Frequenz-basiert)
• Periodicity Detection: Zyklische Muster in Logs
• Audio/Video Search: Similarity in Media-DBs
• Text Analysis: Stylometry, Authorship Detection

Beispiel:

-- Finde ähnliche Zeitreihen via FFT
FOR ts1 IN timeseries
  LET spectrum1 = GPU_FFT(ts1.values)
  FOR ts2 IN timeseries
    FILTER ts1._id != ts2._id
    LET spectrum2 = GPU_FFT(ts2.values)
    LET similarity = GPU_SPECTRAL_SIMILARITY(spectrum1, spectrum2)
    FILTER similarity > 0.9
    RETURN {ts1, ts2, similarity}

Performance:

• CPU FFT: 1,000 FFTs/Sekunde
• GPU FFT: 500,000+ FFTs/Sekunde
• Speedup: 500x

---

2.2 Wavelet Transform

Was ist es?

• Multi-Scale Analyse (Zeit + Frequenz gleichzeitig)
• Besser als FFT für nicht-stationäre Signale
• Edge Detection, Denoising

GPU-Implementierung:

class GPUWaveletAnalyzer {
public:
    enum class WaveletType {
        HAAR, DAUBECHIES, SYMLET, COIFLET
    };
    
    // Continuous Wavelet Transform
    std::vector<std::vector<double>> cwt_GPU(
        const std::vector<double>& signal,
        WaveletType wavelet,
        int scales
    );
    
    // Multi-Resolution Analysis
    struct MRAResult {
        std::vector<std::vector<double>> approximations;
        std::vector<std::vector<double>> details;
    };
    
    MRAResult multiResolutionAnalysis_GPU(
        const std::vector<double>& signal,
        int levels
    );
};

ThemisDB Use Cases:

• Multi-Scale Pattern Search: Patterns auf verschiedenen Zeitskalen
• Compression: Wavelet-basierte Daten-Kompression
• Denoising: Rauschunterdrückung in Zeitreihen
• Edge Detection: Changepoint Detection

Performance:

• CPU: 100 Wavelets/Sekunde
• GPU: 20,000+ Wavelets/Sekunde
• Speedup: 200x

---

2.3 Kalman Filter

Was ist es?

• Optimaler State Estimator
• Sensor Fusion
• Prediction mit Noise

GPU-Implementierung:

class GPUKalmanFilter {
public:
    struct KalmanState {
        Eigen::VectorXd state;
        Eigen::MatrixXd covariance;
    };
    
    // Batch Kalman filtering für viele Zeitreihen
    std::vector<std::vector<KalmanState>> batchFilter_GPU(
        const std::vector<std::vector<double>>& measurements,
        const Eigen::MatrixXd& A,  // State transition
        const Eigen::MatrixXd& H,  // Observation model
        const Eigen::MatrixXd& Q,  // Process noise
        const Eigen::MatrixXd& R   // Measurement noise
    );
};

ThemisDB Use Cases:

• State Estimation: System State Tracking
• Prediction: Short-term Forecasting
• Sensor Fusion: Combine multiple data sources
• Smoothing: Denoising von Metriken

Performance:

• CPU: 500 Filters/Sekunde
• GPU: 50,000+ Filters/Sekunde
• Speedup: 100x

---

3. WIRTSCHAFT/ML-METHODEN

3.1 Spectral Clustering

Was ist es?

• Graph-basiertes Clustering
• Nutzt Eigenvektoren der Laplace-Matrix
• Findet nicht-konvexe Cluster

GPU-Implementierung:

class GPUSpectralClustering {
public:
    // Spectral Clustering auf GPU
    std::vector<int> cluster_GPU(
        const SparseMatrix& affinityMatrix,
        int numClusters,
        int numEigenvectors
    );
    
    // Für Graphen: Community Detection
    std::vector<std::vector<int>> detectCommunities_GPU(
        const PropertyGraph& graph,
        int numCommunities
    );
};

ThemisDB Use Cases:

• Community Detection: Social Networks, Knowledge Graphs
• Customer Segmentation: Market Analysis
• Document Clustering: Text Analytics
• Recommendation: Similar Item Groups

Performance:

• CPU: 10-100 Nodes/Sekunde
• GPU: 10,000+ Nodes/Sekunde
• Speedup: 100x+

---

3.2 Dynamic Time Warping (DTW)

Was ist es?

• Similarity Measure für Zeitreihen unterschiedlicher Länge
• Elastisches Matching
• Spracherkennung, Gesten-Erkennung

GPU-Implementierung:

class GPUDynamicTimeWarping {
public:
    // Batch DTW distance computation
    std::vector<std::vector<double>> batchDTW_GPU(
        const std::vector<std::vector<double>>& series1,
        const std::vector<std::vector<double>>& series2,
        int windowSize = -1  // Sakoe-Chiba band
    );
    
    // DTW-based KNN search
    std::vector<std::vector<int>> dtwKNN_GPU(
        const std::vector<double>& query,
        const std::vector<std::vector<double>>& database,
        int k
    );
};

ThemisDB Use Cases:

• Pattern Search: Flexible Sequence Matching
• Similarity Search: Similar Zeitreihen (unterschiedliche Länge)
• Gesture Recognition: User Behavior Patterns
• Anomaly Detection: Abnormal Sequences

Performance:

• CPU: 100 DTW/Sekunde
• GPU: 10,000+ DTW/Sekunde
• Speedup: 100x

---

3.3 Tensor Decomposition (Tucker, CP)

Was ist es?

• Multidimensionale Matrix-Faktorisierung
• Pattern Discovery in höheren Dimensionen
• Empfehlungssysteme, Knowledge Graphs

GPU-Implementierung:

class GPUTensorDecomposition {
public:
    // CP Decomposition (CANDECOMP/PARAFAC)
    struct CPDecomposition {
        std::vector<Eigen::MatrixXd> factors;
        int rank;
    };
    
    CPDecomposition cpDecomposition_GPU(
        const Tensor& tensor,
        int rank,
        int maxIter = 100
    );
    
    // Tucker Decomposition
    struct TuckerDecomposition {
        Tensor core;
        std::vector<Eigen::MatrixXd> factors;
    };
    
    TuckerDecomposition tuckerDecomposition_GPU(
        const Tensor& tensor,
        const std::vector<int>& ranks
    );
};

ThemisDB Use Cases:

• Knowledge Graph Completion: Missing Links Prediction
• Recommendation: User-Item-Context Tensors
• Multi-Relational Analysis: Complex Entity Relationships
• Pattern Mining: Hidden Patterns in Multi-Dimensional Data

Performance:

• CPU: Minuten für große Tensoren
• GPU: Sekunden
• Speedup: 50-200x

---

4. CROSS-DOMAIN INTEGRATION

4.1 Hybride Pattern Matching Pipeline

class GPUHybridPatternMatcher {
public:
    // Kombiniert FFT, DTW und Anomaly Detection
    struct PatternMatchResult {
        std::vector<int> matches;
        std::vector<double> scores;
        std::vector<double> anomalyScores;
    };
    
    PatternMatchResult findSimilarPatterns_GPU(
        const std::vector<double>& query,
        const std::vector<std::vector<double>>& database,
        int k,
        bool useFFT = true,
        bool useDTW = true,
        bool detectAnomalies = true
    );
};

4.2 Multi-Method Consensus

// Ensemble von mehreren Methoden
class GPUEnsembleAnalyzer {
public:
    struct EnsembleResult {
        std::vector<double> consensusScores;
        std::map<std::string, std::vector<double>> methodScores;
        double confidence;
    };
    
    EnsembleResult analyze_GPU(
        const std::vector<double>& data,
        const std::vector<std::string>& methods  // ["fft", "dtw", "isolation_forest"]
    );
};

---

5. IMPLEMENTIERUNGSPLAN

Phase 1: Foundation (4 Wochen) - P0

• CUDA/Vulkan Backend (Done)
• Faiss GPU (Done)
• Time Series Analysis (ARIMA auf GPU)
• Anomaly Detection (Isolation Forest auf GPU)
• FFT (cuFFT Integration)

Phase 2: Advanced Analytics (6 Wochen) - P1

• Spectral Clustering (für Community Detection)
• Monte Carlo Simulation
• Wavelet Transform
• Dynamic Time Warping

Phase 3: Specialized Methods (8 Wochen) - P2

• Kalman Filter
• Hidden Markov Models
• Tensor Decomposition
• Hybrid Ensemble Methods

---

6. LIBRARIES & TOOLS

GPU Libraries

• cuFFT: NVIDIA FFT Library
• cuBLAS: Linear Algebra
• cuSPARSE: Sparse Matrix Operations
• cuSOLVER: Linear Solvers
• cuRAND: Random Number Generation (Monte Carlo)
• Thrust: GPU STL-like Algorithms

Analytics Libraries

• cuML: RAPIDS ML Library (Clustering, Anomaly Detection)
• cuSignal: Signal Processing on GPU
• cuGraph: Graph Analytics on GPU
• cuDF: GPU DataFrame (Pandas-like)

Integration

# CMakeLists.txt
find_package(CUDAToolkit REQUIRED)
find_package(RAPIDS COMPONENTS cuML cuGraph cuSignal)

target_link_libraries(themis_core
    CUDA::cufft
    CUDA::cublas
    CUDA::cusparse
    RAPIDS::cuml
    RAPIDS::cugraph
    RAPIDS::cusignal
)

---

7. USE CASE MATRIX

Use Case	Methode	Speedup	Business Value
Fraud Detection	Isolation Forest + ARIMA	50x	Hoch
Time Series Search	FFT + DTW	100x	Hoch
Community Detection	Spectral Clustering	50x	Mittel
Risk Analysis	Monte Carlo	1000x	Hoch
Pattern Mining	Wavelet + Tensor	100x	Mittel
Forecasting	ARIMA + Kalman	100x	Hoch
Anomaly Detection	IF + DBSCAN + HMM	50x	Hoch

---

8. EMPFEHLUNG

✅ IMPLEMENTIEREN - Hohe Priorität

Quick Wins (4-6 Wochen):

1. Time Series Analysis (ARIMA) - Sofort verwendbar für Monitoring
2. Anomaly Detection (Isolation Forest) - Fraud Detection, Security
3. FFT (cuFFT) - Pattern Matching Boost

Medium-Term (6-12 Wochen): 4. Spectral Clustering - Community Detection 5. Monte Carlo - Risk Analytics 6. DTW - Flexible Sequence Matching

ROI-Erwartung

• Kosten: $150K (6 Monate Development)
• Nutzen:
  • 50-1000x Performance für spezifische Workloads
  • Neue Kunden (Fintech, Analytics, IoT)
  • Unique Features vs. Konkurrenz
• Break-Even: 12-18 Monate

---

Fazit: Diese Methoden sind hochrelevant für ThemisDB! GPU-Beschleunigung bringt massive Performance-Gewinne (50-1000x) und erschließt neue Use Cases in Finanz, IoT, Analytics.

Letzte Aktualisierung: 20. November 2025