Inner force group for multiple time stepping¶
What it does¶
A SlicedNonbondedForce can place a short-range, force-switched copy of its direct-space pair
interactions in a separate inner force group, so that a multiple time-step integrator can advance it
with a small step while the remainder (the rest of direct space, the reciprocal-space sum and its exclusion
corrections) is advanced with a large one. For a pair at distance \(r\) with bare potential \(V(r)\)
(Lennard-Jones plus Coulomb, scaled by the slice’s parameters), the inner force is
with \(S = 1\) for \(r \le r_s\) and \(S = 0\) for \(r \ge r_c\), where \(r_s\) and \(r_c\) are the inner switching and cutoff distances. The inner energy is the potential \(\hat V\) whose gradient is this force, shifted so that \(\hat V(r_c) = 0\) [6]; the direct-space group reports \(V - \hat V\) and the corresponding force. Every group therefore has an energy consistent with its force, and the groups add up to the unsplit result. The same applies to 1-4 exceptions, and scaling parameters, their derivatives and parameter offsets apply to both parts. The closed form of \(\hat V\) used by all platforms is derived in Theory. In a decapped slice (Capped Lennard-Jones potential), the potential below \(\sigma\) is the capped one plus the decapping term instead of the bare one; since \(\sigma \le r_s\), the inner group takes all of it there, and the remainder is unchanged.
Setting it up¶
force = nbs.SlicedNonbondedForce(nonbonded, 2)
force.setForceGroup(2) # direct-space remainder; reciprocal space goes there too
force.setInnerForceGroup(1)
force.setInnerSwitchingDistance(0.5*unit.nanometer)
force.setInnerCutoffDistance(0.8*unit.nanometer)
# bonded forces in group 0; steps of 90, 3 and 0.5 fs
integrator = mm.MTSIntegrator(90*unit.femtoseconds, [(2, 1), (1, 30), (0, 180)])
If the reciprocal-space sum is also moved to a group of its own with setReciprocalSpaceForceGroup, call
setReciprocalExclusions(True) so that the exclusion corrections go with it (Reciprocal-space force group and exclusion corrections) and the
slow group has no fast intramolecular component.
Restrictions¶
The inner force group must differ from the force group of the force and, with Ewald, PME or LJPME, from its reciprocal-space force group.
The distances must satisfy \(0 < r_s < r_c \le\) cutoff distance and, when the Lennard-Jones switching function is used, \(r_c \le\) switching distance: the inner force is the bare Lennard-Jones force times \(S(r)\), which beyond the switching distance would exceed the switched force and leave the remainder with a correction of opposite sign.
With decapped slices (Capped Lennard-Jones potential), the inner group takes all of the capped and decapping terms below \(\sigma\), so the \(\sigma\) of every Lennard-Jones pair of a Lennard-Jones-decapped slice and of every charged pair of a Coulomb-decapped slice cannot exceed \(r_s\).
The inner force group requires the direct space to be included (the default; see
setIncludeDirectSpace).The inner force group, switching distance and cutoff distance are fixed when a openmm.Context is created; changing them afterwards takes effect only after the Context’s
reinitialize()method is called.On the CUDA and OpenCL platforms, all nonbonded interactions in one force group must use the same cutoff, so a Context fails to be created if the inner force group also contains another cutoff-based nonbonded force, such as a openmm.CustomNonbondedForce, with a different cutoff. Put the inner force group in a group of its own, or in one whose other nonbonded forces use the inner cutoff.
Performance¶
On the CUDA and OpenCL platforms, the cost of an inner-group evaluation depends little on the inner cutoff,
because the inner kernels traverse the neighbor list built for the full cutoff and only skip the pairs
beyond \(r_c\). The inner group is therefore not much cheaper than the direct space it is carved from, which
limits the speedup of multiple time stepping. The --inner-group mode of devtools/benchmarks/benchmark.py
measures it.
