Data Compression for Optimization of a Molecular Dynamics System: Preserving Basins of Attraction

Abstract

Understanding the evolution of atomistic systems is essential in various fields such as materials science, biology, and chemistry. The gold standard for these calculations is molecular dynamics, which simulates the dynamical interaction between pairs of molecules. The main challenge of such simulation is the numerical complexity, given a vast number of atoms over a long time scale. Furthermore, such systems often contain exponentially many optimal states, and the simulation tends to get trapped in local configurations. Recent developments leverage the existing temporal evolution of the system to improve the stability and scalability of the method; however, they suffer from large data storage requirements. To efficiently compress the data while retaining the basins of attraction, we have developed a framework to determine the acceptable level of compression for an optimization method by application of a Kantorovich-type theorem, using binary digit rounding as our compression technique. Choosing the Lennard-Jones potential function as a model problem, we present a method for determining the local Lipschitz constant of the Hessian with low computational cost, thus allowing the use of our technique in real-time computation.