Mathematical advance makes molecular simulations much faster

Mathematical advance makes molecular simulations much faster

A classical mathematical function allows simulations of atoms and molecules to run several times faster on supercomputers while keeping full accuracy.

GP
Giulio Prisco
Jun 25, 2026
2 min read

More than one-fifth of the computing time on the world’s 500 fastest supercomputers goes to molecular dynamics simulations. These computer models track how atoms and molecules move over time. The simulations help design new materials, study how drugs interact with proteins, and understand how proteins fold into their working shapes.

Researchers at the Simons Foundation’s Flatiron Institute created a new method that makes these simulations run between two and a half and seven times faster. The improvement comes from a classical mathematical function known as prolate spheroidal wave functions. For the widely used GROMACS software, the new approach delivered a fivefold speed increase when run at high accuracy. The method can be added easily to existing programs, so it could quickly reduce the time and energy needed for this type of work.

Improving calculations of forces between atoms

The main difficulty in molecular dynamics simulations is calculating the pushing and pulling between charged particles inside molecules. These long-range electrostatic forces require checking interactions across a large box of atoms. Earlier shortcuts, such as the fast Fourier transform and the fast multipole method, helped reduce the work, but the calculations still used large amounts of computer time.

The new method uses prolate spheroidal wave functions to decide how to separate short-range and long-range forces and how to spread atomic charges onto a grid for the long-range part. These functions are especially good at staying focused in a small area while remaining smooth, which reduces errors and speeds up the work. The researchers tested the approach on systems including water molecules, an immune-related protein, and a lithium-ion solution used in batteries. In every case, the simulations finished several times faster than before.

The code has already been accepted into major simulation packages such as LAMMPS. Experts not involved in the work say the advance could meaningfully cut computing demands across many areas of science that depend on these simulations.

This research is published in Nature Communications.

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