Accelerating Molecular Dynamics Simulations with Population Annealing

Population annealing is a powerful tool for large-scale Monte Carlo simulations. We adapt this method to molecular dynamics simulations and demonstrate its excellent accelerating effect by simulating the folding of a short peptide commonly used to gauge the performance of algorithms. The method is compared to the well established parallel tempering approach and is found to yield similar performance for the same computational resources. In contrast to other methods, however, population annealing scales to a nearly arbitrary number of parallel processors, and it is thus a unique tool that enables molecular dynamics to tap into the massively parallel computing power available in supercomputers that is so much needed for a range of difficult computational problems.

Figure 1

Ramachandran plot for the amino acid GLY-2 of met-enkephalin at $T_0=700\mathrm{K}$ obtained from a canonical simulation.

Figure 2

Measured temperature $T_{\mathrm{m}}$ vs the heat-bath temperature $T$ for population annealing (PA) simulations with $\theta =1000$ and $\theta =4375$ as well as for PA with resampling turned off (“anneal”).

Figure 3

Energy histograms at the lowest temperature, $T=200\mathrm{K}$, as obtained from the population annealing (PA), parallel tempering (PT), PA without resampling (“anneal”), and canonical simulations, respectively.

Figure 4

Ramachandran plot for GLY-3 at $T=200\mathrm{K}$ obtained from the population annealing (PA) and a canonical simulation. The total run time of both methods was 200 ns. The configuration space sampled by PA is far superior to that sampled by a canonical simulation.

Figure 5

Ramachandran plots for (a) GLY-2, (b) GLY-3, and (c) PHE-4 at $T=200\mathrm{K}$ obtained from the population annealing (PA) and parallel tempering (PT) simulations. The total amount of parallel work for each method was the equivalent of 200 ns of MD steps. The fraction of configuration space sampled by the two methods is approximately equivalent.

Figure 6

Speedup $S_p$ for a different number of processors $p$ for the PAMD with $\theta =4375$ and $R=10000$. The solid line corresponds to perfect scaling. In the inset, we show the efficiency $S_p/p$ for the same simulation.

Figure 7

Ramachandran plot for GLY-3 at $T=200\mathrm{K}$ obtained from a population annealing (PA) simulation with $R=2\times {10}^4$ replicas as compared to the parallel tempering (PT) simulation of total run time 200 ns already shown in Fig. 5.