Performance of Hybrid Monte Carlo on Abalone.

Hybrid Monte Carlo is very accurate calculation method of the thermodynamic properties of the substances in the classical molecular mechanics. I would like to announce a significant improvement in the speed of the GPU calculations on the Abalone program.

There is a benchmark on the page

Is there a paper that describes the underlying work?

Unfortunately there is no paper.

However, this is the most common Hybrid Monte Carlo algorithm. The only interesting thing is that it uses an VEFRL Omelyan algorithm as MD step. This algorithm is the fourth order, and if you reduce the length of the step only a few times, then you already reach the machine precision.

When you refer to “machine precision” are we talking single precision or double precision?

If reduce step in 10 times than would be achieved float precision, if in 100 times the double.

I do not know for what in the molecular dynamics can be used trajectory with double precision. However, if it is needed, it is easily achieved by Omelyan algorithms.

I assume the relevant reference for the “VEFRL Omelyan algorithm” is this:
I.P. Omelyan, I.M. Mryglod, R. Folk
Optimized Forest–Ruth- and Suzuki-like algorithms for integration of motion in many-body systems
Computer Physics Communications
Volume 146, Issue 2, 1 July 2002, Pages 188–202

From the preprint,, equation (21) seems to be the relevant computation. If so, it seems very amenable to the application of the FMA (fused multiply-add) operation provided by GPUs. This should help somewhat with maintaining accuracy by reducing round-off errors and giving some protection against subtractive cancellation.

Yes, I mean namely this algorithm. This is not a fast algorithm, but very accurate. Fast are multi-step algorithms, which Abalone also has.

Many thanks to NVIDIA team for the providing GeForce GTX 980 for testing.

In some cases, acceleration reaches 120 times: