Time Integration Algorithms

Since some years, I am developing optimized modern time integration algorithms to speed up molecular dynamics simulations without sacrificing accuracy (or to make them more accurate at the same computational cost). This is a topic which has been very much neglected within the last decades. While the methods for energy computation in such simulations have evolved a lot (ab initio MD, polarizable force fields, machine learning, ...), the integration approach is still always the same, namely the Størmer–Verlet algorithm, also known as “velocity Verlet” or “leapfrog” algorithm (these three are identical). There have been previous attempts to improve time integration, such as those by Yoshida or Suzuki, but those have not translated into better efficiency for practical MD simulations.

Together with my colleague Christian Dreßler, I have addressed this issue. We have developed a family of novel time integration algorithms which we have optimized to substantially enhance the performance of MD simulations. Our algorithms are explicit 8-stage Runge–Kutta–Nyström methods that are both symmetric (i.e. time-reversible) and symplectic, ensuring excellent long-term stability and energy conservation. The performance gains are significant: Compared to a MD simulation with a Verlet time step of Δt=0.5 fs, our methods deliver either a 2.5-fold increase in computational speed at the same accuracy, or a 150-fold increase in accuracy (measured in terms of energy conservation) at the same computational cost. Even compared to a Verlet time step of Δt=1.0 fs, our approach still achieves a two-fold speedup at the same accuracy, or a six-fold increase in accuracy using the same resources. As a time integration algorithm, our approach is independent of the underlying computational model, and thus compatible with all flavors of MD, including ab initio MD (AIMD), force field MD, and machine learned interatomic potentials (MLIPs).

There is no paper published yet on this project, we are working on it. A draft with the actual parameters of the novel algorithm as well as some benchmark results will be uploaded here soon. We are also currently working on initial implementations in the Lammps, CP2k, and ORCA program packages.

Please check again in a few weeks. Content will appear during fall 2026.

Timeline:

Date	Notes
Sep 15 2026	I will be giving a talk at the STC conference in Graz. The title of my talk is “Beyond Verlet: Unlocking a 2x Speedup in Molecular Dynamics with Novel Time Integrators”. You can find my abstract here. This is the first time I am presenting this research project to the general public.
Jan 2023	As a side result of my studies in mathematics, I started working on optimizing time integration algorithms for molecular dynamics simulations.