Adaptive multi-stage integrators for optimal energy conservation in molecular simulations Articles uri icon

publication date

  • December 2016

start page

  • 434

end page

  • 449


  • 327

International Standard Serial Number (ISSN)

  • 0021-9991

Electronic International Standard Serial Number (EISSN)

  • 1090-2716


  • We introduce a new Adaptive Integration Approach (AIA) to be used in a wide range of molecular simulations. Given a simulation problem and a step size, the method automatically chooses the optimal scheme out of an available family of numerical integrators. Although we focus on two-stage splitting integrators, the idea may be used with more general families. In each instance, the system-specific integrating scheme identified by our approach is optimal in the sense that it provides the best conservation of energy for harmonic forces. The AIA method has been implemented in the BCAM-modified GROMACS software package. Numerical tests in molecular dynamics and hybrid Monte Carlo simulations of constrained and unconstrained physical systems show that the method successfully realizes the fail-safe strategy. In all experiments, and for each of the criteria employed, the AIA is at least as good as, and often significantly outperforms the standard Verlet scheme, as well as fixed parameter, optimized two-stage integrators. In particular, for the systems where harmonic forces play an important role, the sampling efficiency found in simulations using the AIA is up to 5 times better than the one achieved with other tested schemes. (C) 2016 Elsevier Inc. All rights reserved.


  • Mathematics


  • molecular dynamics; hybrid monte carlo; multi-stage integrators; velocity verlet; adaptive integration; gromacs; constrained hamiltonian-systems; dynamics simulations; differential-equations; numerical integrators; villin headpiece; time steps; algorithm; resonance