Main innovation: the developed Parareal variant ensures stability for long-time simulations (for which standard Parareal is unstable). In addition, it results in a significant efficiency gain.
We designed an adaptive variant of the parareal algorithm. When considering long-time simulations of molecular systems, we have observed that the standard parareal algorithm is unstable. In collaboration with U. Sharma (Freie Universitat Berlin, Germany), we introduced an adaptive variant of the parareal algorithm, specifically tailored to molecular dynamics simulations. The algorithm is adaptive in the sense that the time horizon of the simulation is iteratively adjusted, in order to prevent the algorithm from simulating parts of the trajectory where the accuracy is deemed to be insufficient. A significant gain in efficiency is obtained in comparison to the standard parareal algorithm.
A natural follow-up of this work is to implement this algorithm in LAMMPS (a very well distributed software in the material science community), that will open the way to the simulation of realistic physical systems. This work has been completed in collaboration with D. Perez (Los Alamos Nat. Lab., USA). We combined there a family of machine-learned force fields (for the reference propagator) with classical force fields (for the coarse propagator) and studied the diffusion of atomistic defects in tungsten lattices. On this system of physical interest, we again obtained significant efficiency gains.
The figure below shows that our adaptive parareal algorithm always outperforms, in terms of wall-clock time gain, the vanilla version of parareal. In addition, the gain is robust and independent of the length of the trajectory. This opens the way to using this variant of the algorithm for large-scale MD applications.
The figure below shows the results obtained with our variant for the computation of average residence times of defects in tungsten lattices. These results (in blue) are consistent with the reference results (in orange) and are obtained at a much smaller computational cost.
- F. Legoll, T. Lelièvre, U. Sharma, An adaptive parareal algorithm: application to the simulation of molecular dynamics trajectories, SIAM Journal on Scientific Computing, vol. 44 (1), B146-B176 (2022).
- O. Gorynina, F. Legoll, T. Lelièvre, D. Perez, Combining machine-learned and empirical force fields with the parareal algorithm: application to the diffusion of atomistic defects, Comptes Rendus Mécanique, vol. 351 (1) (special issue on the scientific legacy of Roland Glowinski), in press (2023).