Abstract

PyTorch implementation of the classic Müller-Brown potential energy surface, a computational chemistry benchmark used since 1979. Includes both analytical derivatives and automatic differentiation options, JIT compilation for performance, and molecular dynamics simulation capabilities. Benchmarking shows analytical derivatives provide 3-10x speedups over autograd.

Key Features

  • Dual computation modes: Both analytical derivatives and automatic differentiation
  • Performance optimization: JIT compilation eliminates Python overhead
  • Complete implementation: Includes molecular dynamics and visualization tools
  • Educational focus: Bridges classical computational chemistry with modern ML frameworks

What I Built

Implementation Details

Core implementation efficiently handles the mathematical function:

  • Function evaluation: Potential energy calculation using four Gaussian terms
  • Force computation: Either analytical derivatives or PyTorch autograd
  • Batch processing: Vectorized operations for multiple coordinate sets
  • Device handling: Works on CPU or GPU with appropriate tensor placement

Performance Results

Benchmarking across different batch sizes showed:

  • Analytical derivatives consistently outperform autograd by 3-10x
  • Per-particle computation stays under 1 microsecond for large systems
  • Linear scaling enables processing 100,000+ coordinates efficiently
  • JIT compilation provides significant speedups over pure Python

Molecular Dynamics

Included Langevin dynamics simulations demonstrate the potential’s behavior:

  • Particle motion in different energy basins
  • Thermal fluctuations around local minima
  • Transitions between energy wells
  • Trajectory visualization on the potential surface

Why It Matters

Learning Value

This implementation demonstrates:

  • How to translate mathematical functions into efficient PyTorch code
  • When analytical derivatives are worth the extra implementation effort
  • How JIT compilation can speed up mathematical kernels
  • Integration of classical computational chemistry with modern ML frameworks

Practical Applications

The Müller-Brown potential remains useful for:

  • Testing algorithms: Known surface for validating optimization and sampling methods
  • Educational purposes: Simple 2D system for learning molecular dynamics concepts
  • ML benchmarking: Ground truth potential for testing machine learning models
  • Method development: Reliable test case for new computational approaches

Technical Notes

Implementation focuses on clarity and performance:

  • Clean separation between mathematical formulation and computational details
  • Comprehensive documentation and examples
  • Reproducible benchmarking with all code included
  • Interactive visualizations to understand the energy landscape

This work demonstrates how classic scientific computing problems can benefit from modern frameworks while maintaining computational efficiency.

This implementation is documented in detail in: