(75a) Model and Computational Reduction for Molecular Dynamics of Polymer Systems

A polymer molecular dynamics simulation, composed of multiple polymer chains, is defined by a large collection of discrete atoms, their interactions, and the resulting dynamic trajectories. Due to the high computational burden of simulating many atoms while resolving fast vibrational atomic timescales, the simulation time of a molecular dynamics simulation is typically on the order of nanoseconds, while the relaxation time of the polymer ranges from 1-1000 s. Methods for coarse-graining of molecular simulations, by grouping nearby atoms, have been developed to speed up molecular dynamics simulations (Faller, Muller-Plathe), but due to the complexity of polymer tacticity, the size of the groups may be limited to one monomer. However, much greater speedup is still needed.

Automated method for model reduction and system identification could provide a complementary approach for computational reduction, such as equation-free computing (Kevrekidis). However, identifying an appropriate reduced-order state for equation-free computing remains a challenging problem (Frederix), even for a simple fluid. In this work we propose and demonstrate a modeling method for molecular dynamics simulations of polymers, which combines features from equation-free computing with polymer coarse-graining. A modified local feature analysis (Atick, Wriggers, Xue) is applied to molecular dynamics simulations, to automatically identify "seed" atoms, based on correlations in the dynamic motion of the atoms. Unlike typical coarse-graining methods, the atom groups defined by these seeds may or may not be on the same polymer chain. We then apply time-series techniques to propagate forward the trajectories of the seed atoms to the future time T. The positions of all atoms can then be reconstructed via the local feature analysis. We define this process, from atomistic simulation to the recovery of the system at time T, as one model iteration.

At each iteration, the local feature analysis is repeated, such that the seed atoms may change over time as the polymer conformation changes. Only simple matrix calculations are required to calculate the local feature analysis and its reconstruction, so that the primary computation is associated with the short molecular dynamics simulations run in each simulation.

The proposed model reduction scheme is evaluated through two systems. One is a simple mass-spring-damper system with 10 masses. The proposed approach is shown to recover the system dynamics at future time accurately. The other one is a simulated atactic multi-chain polymer system. We analyze the wide angle x-ray diffraction pattern, as well as the computation time of both the original system and the reduced system, to show the accuracy and the effectiveness of the proposed algorithm.

Bibliography

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