Extending molecular simulation time scales: Parallel in time integrations for high-level quantum chemistry and complex force representations

Abstract

Structure and dynamics of the hydration shells of the ion from ab initio molecular dynamics and combined ab initio and classical molecular dynamics simulations The Journal of Chemical Physics 132, 194502 (2010) Parallel in time simulation algorithms are presented and applied to conventional molecular dynamics (MD) and ab initio molecular dynamics (AIMD) models of realistic complexity. Assuming that a forward time integrator, f (e.g., Verlet algorithm), is available to propagate the system from time t i (trajectory positions and velocities, the dynamics problem spanning an interval from t 0 . . . t M can be transformed into a root finding problem,for the trajectory variables. The root finding problem is solved using a variety of root finding techniques, including quasi-Newton and preconditioned quasi-Newton schemes that are all unconditionally convergent. The algorithms are parallelized by assigning a processor to each time-step entry in the columns of F(X). The relation of this approach to other recently proposed parallel in time methods is discussed, and the effectiveness of various approaches to solving the root finding problem is tested. We demonstrate that more efficient dynamical models based on simplified interactions or coarsening time-steps provide preconditioners for the root finding problem. However, for MD and AIMD simulations, such preconditioners are not required to obtain reasonable convergence and their cost must be considered in the performance of the algorithm. The parallel in time algorithms developed are tested by applying them to MD and AIMD simulations of size and complexity similar to those encountered in present day applications. These include a 1000 Si atom MD simulation using Stillinger-Weber potentials, and a HCl + 4H 2 O AIMD simulation at the MP2 level. The maximum speedup ( serial execution time parallel execution time ) obtained by parallelizing the Stillinger-Weber MD simulation was nearly 3.0. For the AIMD MP2 simulations, the algorithms achieved speedups of up to 14.3. The parallel in time algorithms can be implemented in a distributed computing environment using very slow transmission control protocol/Internet protocol networks. Scripts written in Python that make calls to a precompiled quantum chemistry package (NWChem) are demonstrated to provide an actual speedup of 8.2 for a 2.5 ps AIMD simulation of HCl + 4H 2 O at the MP2/6-31G* level. Implemented in this way these algorithms can be used for long time high-level AIMD simulations at a modest cost using machines connected by very slow networks such as WiFi, or in different time zones connected by the Internet. The algorithms can also be used with programs that are already parallel. Using these algorithms, we are able to reduce the cost of a MP2/6-311++G(2d,2p) simulation that had reached its maximum possible speedup in the parallelization of the electronic structure calculation from 32 s/time step to 6.9 s/time step.

A stable parareal-like method for the second order wave equation

“…Recall that the elements in the columns of F and G consist of the spatial gradients and weighted time derivatives of the solutions on the respective fine and coarse grid, and that the 2 norm corresponds to the discrete wave energy (9). Therefore, we look for a unitary matrix so that the discrete wave energy of the coarse solutions is preserved at different times.…”

“…Let us denote the square root of wave energy as E([U,U ]) := E([U,U ]), where E is defined in (9). Thus,…”

Using multiscale preconditioning to accelerate the convergence of iterative molecular calculations

“…Here we have used a change of variables specifically designed to take advantage of existing, inexpensive coarse-grained models. The parareal method 21,22 which speeds direct integration of evolutionary differential equations using inexpensive CG methods can be cast in a very similar framework as can nonlinear (and linear) multigrid iteration. 23,24 We expect for certain systems that it will be advantageous to modulate the extent to which the CG model contributes to the state update.…”

Path-accelerated stochastic molecular dynamics: Parallel-in-time integration using path integrals

“…Most approaches [14][15][16][17] are based on a prediction-correction paradigm that combines fine (i.e., accurate and expensive) and coarse (i.e., inaccurate and inexpensive) solvers to iteratively refine approximations of a trajectory in a convergent and parallel-intime fashion. A range of coarse solvers and iteration schemes have been employed to evaluate MD trajectories a) Correspondence: tfm@caltech.edu of molecular systems with parallelization in the time domain [18][19][20][21][22] , leading to order-of-magnitude reductions in the wall-clock time-to-solution with respect to sequential integration at the fine level of accuracy. Schemes for approximate long-timescale integration via trajectory splicing are an alternative route to parallelization in time, yielding accurate time evolution for systems that exhibit strong timescale separation on well-characterized regions of the potential energy landscape 23 .…”