Symplectic Integrator on GPUs

Demonstrating mathematical integrity under GPU parallelization and reduced precision.

View the Project on GitHub OleBo/SymplecticIntegrator

Project Completion Summary

✅ Completed

Phase 1: Project Structure & CPU Baseline

Phase 2: GPU Foundation

Phase 3: Documentation

Phase 4: Build & Test Infrastructure

📊 Project Statistics

Category Count
Python files 4
CUDA/C++ files 2
Header files 2
Documentation files 4
Jupyter notebooks 1
Configuration files 4
Total files 17

🎯 What You Have

Immediately Usable

# Run CPU benchmark
cd src/cpu
python benchmark.py

# Interactive analysis
cd notebooks
jupyter notebook 01_cpu_benchmark.ipynb

Mathematical Foundation

GPU Ready

Documentation

🚀 Next Steps (Recommended Order)

Immediate (1-2 hours)

  1. Run CPU benchmark 
    cd src/cpu
python benchmark.py
    • Generates energy comparison plots
    • Shows symplectic advantage
    • Validates baseline implementations
  2. Explore analysis notebook 
    cd notebooks
jupyter notebook 01_cpu_benchmark.ipynb
    • Interactive energy analysis
    • Phase space visualization (template)
    • Statistical comparison

Short-term (1 week)

  1. Test GPU build (requires CUDA) 
    mkdir build && cd build
cmake ..
make
  2. Profile GPU kernels 
    nvprof ./build/example
  3. Add more analysis
    • Phase space trajectories plot
    • Lyapunov exponent estimation
    • Ensemble statistics

Medium-term (2-4 weeks)

  1. GPU optimization
    • Profile memory bandwidth
    • Tune block/grid sizes
    • Measure sustained TFLOPS
    • Compare kernel versions
  2. Extensions
    • Adaptive timestep
    • Mixed precision (FP32 pos, FP64 energy)
    • Higher-order symplectic (6th order)
    • Different Hamiltonian systems
  3. Performance comparison
    • CPU vs GPU timing
    • Scaling with trajectory count
    • Memory bandwidth utilization
    • Performance summary paper

Long-term (1+ month)

  1. Advanced features
    • Poincaré section visualization
    • Chaos detection heuristics
    • Hybrid multi-GPU execution
    • Real application (molecular dynamics, astrophysics)

📁 Project Structure Reference

SymplecticIntegrator/
├── .github/
│   └── copilot-instructions.md      # Project guidelines
├── include/
│   ├── henon_heiles.h               # System definitions
│   └── integrators.h                # GPU/CPU API
├── src/
│   ├── cpu/
│   │   ├── __init__.py
│   │   ├── integrators.py           # ⭐ Main CPU code
│   │   ├── analysis.py              # Energy analysis
│   │   ├── henon_heiles.py          # Utilities
│   │   └── benchmark.py             # ⭐ Run this first!
│   └── gpu/
│       ├── integrators.cu           # GPU kernels
│       └── example.cpp              # Example usage
├── notebooks/
│   └── 01_cpu_benchmark.ipynb       # Interactive analysis
├── tests/
│   └── CMakeLists.txt
├── data/                            # Output directory
├── build/                           # Build output
├── QUICKSTART.md                    # First-steps guide
├── README.md                        # Full documentation
├── ARCHITECTURE.md                  # Design deep-dive
├── CMakeLists.txt                   # CUDA build system
├── requirements.txt                 # Python deps
├── .gitignore
└── TODO.md                          # This file

💡 Key Insights

What Makes This Project Special

  1. Mathematical Integrity
    • Shows you understand structure preservation
    • Demonstrates long-term numerical stability
    • Not just “make it run fast”
  2. GPU Specialization
    • Perfect embarrassingly-parallel problem
    • Independent trajectories = transparent scaling
    • Optimal memory access patterns
    • Minimal synchronization overhead
  3. Clear Differentiation
    • Most projects: GEMM, CNNs, LSTMs
    • This project: Mathematical structures + GPU acceleration
    • Signals deep technical understanding

For Interviews/Presentations

Elevator pitch:

“I implemented a GPU-accelerated symplectic integrator for Hamiltonian systems. This demonstrates three key capabilities: (1) understanding of structure-preserving algorithms from mechanics, (2) ability to map mathematical problems to GPU parallelism, and (3) focus on correctness over mere performance.”

Key talking points:

🧪 Verification Checklist

🎓 Learning Resources

  1. Structure-Preserving Integration
    • Leimkuhler & Reich: “Simulating Hamiltonian Dynamics” (2004)
    • Ruth: “A Canonical Integration Technique” (1983)
  2. Chaotic Dynamics
    • Henon & Heiles: “The applicability of the third integral of motion” (1964)
    • Strogatz: “Nonlinear Dynamics and Chaos” (2014)
  3. GPU Programming
    • NVIDIA CUDA C++ Programming Guide
    • GPU Performance Analysis with NSight Compute

Video Resources

🤝 Contributing

Future enhancements welcome:

  1. Implement other Hamiltonian systems
  2. Add adaptive timestep control
  3. Create visualization dashboard
  4. Performance benchmarking suite
  5. Mixed-precision arithmetic
  6. MPI + GPU multi-GPU version

📝 Notes

Questions to Explore

Future Ideas

✨ Summary

What you’re ready to do right now:

  1. Run CPU benchmark: python src/cpu/benchmark.py
  2. View analysis: jupyter notebook notebooks/01_cpu_benchmark.ipynb
  3. Study code: Check src/cpu/integrators.py for clean algorithm implementations
  4. Build GPU: mkdir build && cd build && cmake .. && make

What this demonstrates:

Get started: Run python src/cpu/benchmark.py and check data/energy_drift_comparison.png

The energy plot is your “wow” moment—watch how symplectic stays stable while Euler explodes. That’s the whole story.