Adaptively Restrained Particle Simulations

Interaction potentials used in particle simulations are typically written as a sum of terms which depend on just a few relative particle positions. Traditional simulation methods move all particles at each time step, and may thus spend a lot of time updating interparticle forces. In this Letter we introduce adaptively restrained particle simulations (ARPS) to speed up particle simulations by adaptively switching on and off positional degrees of freedom, while letting momenta evolve. We illustrate ARPS on several numerical experiments, including (a) a collision cascade example that demonstrates how ARPS make it possible to smoothly trade between precision and speed and (b) a polymer-in-solvent study that shows how one may efficiently determine static equilibrium properties with ARPS.

Figure 1

Phase portrait of the adaptively restrained harmonic oscillator (${\epsilon }_1^r=0.5$, ${\epsilon }_1^f=0.8\mathrm{kcal}/\mathrm{mol}$). In the full-dynamics region, trajectories remain unperturbed. In the restrained-dynamics region, positions are constant although momenta evolve.

Figure 2

Adaptively restrained simulations of a periodic 3D box of 21 952 Argon particles, with two different pairs of thresholds ($NVE$ ensemble). The total adaptive energies are stable for both simulations, even when the average number of active particles $⟨N_{\mathrm{act}}⟩$ is greatly reduced. The decrease in the average number of updated forces $⟨N_F⟩$ results in significant speed-ups.

Figure 3

Simulating a collision cascade with controlled precision (thresholds in $\mathrm{kcal}/\mathrm{mol}$, NVE ensemble). AR simulations allow us to smoothly trade between precision and speed. Even for large speed-ups (up to 10 times), the features of the picture are extremely well preserved.

Figure 4

Radial distribution functions for an Argon system (periodic 3D box, 343 particles, $NVT$ ensemble). Even though the AR simulation has significantly modified the system’s dynamics (see $⟨N_{\mathrm{act}}⟩$), the curves coincide.

Figure 5

Computing the hydrodynamic radius of a solvated polymer (NVT ensemble). Full-dynamics simulations reduce the variance more at each time step (top), but AR simulations perform many more time steps, so that they reduce the variance faster in wall-clock time (bottom). For any target precision, AR simulations compute the hydrodynamic radius four times faster than full-dynamics simulations.