amber-developers: How to compute H2O:H2O nonbonded forces 80% faster than PMEMD9

From: David Cerutti <>
Date: Wed, 13 Dec 2006 14:43:29 -0800 (PST)

    I've been playing with lookup tables and linear interpolation for
nonbonded force computations using a simple, homemade molecular dynamics
engine that I plan to use to parameterize a new water model. My lookup-
based non-bonded force computation is considerably faster than AMBER9's
PMEMD module, and will work for general pairwise potential functions.
Taking a large box of water as a text case, my computation seems to go
about 80% faster than PMEMD if I use linear interpolation, and
cubic-spline interpolation seems like it would incur a minor additional
cost (overall performance perhaps 70% faster than PMEMD). Bear in mind
that this enhancement applies to water:water interaction computation only;
other interactions would be computed in the conventional manner.
    The key to my success was to make lookup tables for each of the
interactions that might be found in the water, by far the most ubiquitous
substance in the simulation.
    I re-image the residues based on the location of a "central atom",
split the primary simulation cell into sub-cells based on the cutoff and
the maximum size of a water molecule (defined by the rigid O-H bond in my
case, although one could extend this to work with flexible waters by
making some assumption that the bond won't stretch more than perhaps
0.5A), then replicate the peripheral sub-cells to satisfy PBCs. (I find,
as you probably know, that this is much faster than computing the PBCs on
the fly.) I then loop over the sub-cells, determining first whether two
residues' central atoms (again, the water oxygens) are close enough to
possibly have atoms within the nonbonded cutoff and, if they are,
computing their interactions via linear interpolation from finely-spaced
tables indexed by the squared distance.
    To save some memory, I have a "high-resolution" table (sampled every
0.005 A^2) that extends to about 6A and is used to compute interactions
when two central atoms are within about 4A of one another, and a
"low-resolution" (sampled every 0.05 A^2) table that is used to compute
longer-range interactions. (In this way, I can better vectorize the
innermost loop--computing interactions between all atoms of water A and
water B.) For now, I'm doing linear interpolation using double precision
in the lookup table, but this is of course rather mismatched. A quick
adjustment suggests that the lookup tables could be modified to encode
cubic splines with an appropriate adjustment to the resolution, at a 10%
cost in the overall performance. NAMD uses lookup tables with spline
interpolation an even lower resolution of ~0.06A^2; it merely fails to
treat the ubiquitous water in a special manner.
    I've profiled the code somewhat, but again I don't have many
optimizations other than a well-planned indexing system for the residues
and a nice set of lookup tables. The speed of the program seems to be
quite insensitive to the size of lookup table, even on a four-year old
processor with only 512kB L2 cache. Whether I double the resolution or
cut it in half, the cpu time changes ~1%. The (linear interpolant) lookup
tables for all atom types combined require ~200kB of memory, but I think I
save more time and memory by simply foregoing the water:water neighbor
    Perhaps this simple method could be implemented in the next PMEMD?

Received on Thu Dec 14 2006 - 05:00:03 PST
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