Coarse Graining

In aKMC simulations where there are vastly different rates, the simulation can get stuck in a group of states connected by relatively fast rates. In order to explore slower transitions, a prohibitively large number of KMC steps may be needed. In order to circumvent this problem, eOn implements two methods.

Note

AS-KMC and MCAMC cannot be used simultaneously.

Monte Carlo with Absorbing Markov Chains (MCAMC)

The first method, projective dynamics, described in Novotny [CG_Nov01], groups states that are joined by fast rates into “superbasins”. Information about transitions between states in a superbasin is lost, but the rates for transitions across a superbasin are correct.

Accelerated Superbasin Kinetic Monte Carlo (AS-KMC)

The second method, accelerated superbasin kinetic Monte Carlo (AS-KMC) of Voter [CG_Vot97], artificially raises low barriers. The dynamics between states connected by fast rates are simulated, but an error is introduced in the dynamics direction and time.

The basic process of AS-KMC involves gradually raising process barriers found to be inside of a superbasin such that exiting from the basin gradually becomes more likely. The method is designed to raise all the barriers in the superbasin simultaneously. Once a particular barrier has been crossed a certain number of times, \(N_f\) (more on determining \(N_f\) shortly), a check is performed to determine whether or not the current state is part of a superbasin. This is called the Superbasin Criterion.

In the Superbasin Criterion, a search is performed, originating at the current state and proceeding outward through all low-barrier processes to adjacent states, and then through all low-barrier processes from each of these states, etc. For each low-barrier process found, if the process has been followed fewer than \(N_f\) times, the Superbasin Criterion fails and no barriers are raised.

Thus, in the outward-expanding search from the originating state, the search continues until either a low-barrier process has been seen fewer than \(N_f\) times (and the Criterion fails) or until all connected low-barrier processes have been found and have been crossed at least \(N_f\) times (the edges of the superbasin are then defined and the Criterion passes). If the Superbasin Criterion passes, all the low-barrier processes (each of which as been crossed \(N_f\) times) are raised.

Several parameters dictate the functioning of the AS-KMC method. These parameters dictate how much the barriers are raised each time the Superbasin Criterion passes(eon.schema.CoarseGrainingConfig.askmc_barrier_raise_param), what defines a “low-barrier” for use in the Superbasin Criterion(eon.schema.CoarseGrainingConfig.askmc_high_barrier_def), and the approximate amount of error the user might expect in eventual superbasin exit direction and time compared to normal KMC simulation (eon.schema.CoarseGrainingConfig.askmc_confidence).

Optional AMSEl discover/decide gate

When MCAMC superbasins are active, an optional pre-step gate can call amsel.discover_decide_status on the superbasin process graph before Superbasin.step. Enable it under [amsel] (default off):

[amsel]
discover_decide = True
e_min_init = 0.5
e_min_step = 0.05
e_min_floor = 0.05
cv_threshold = 10.0

If the amsel Python package is not installed, the gate is a no-op and legacy MCAMC behaviour is unchanged. Status outcomes:

  • accepted / retightened — proceed with MCAMC as usual

  • split_required — restrict the superbasin to the primary transient set (entry state is always retained; membership is persisted via write_data)

  • rejected_no_metastable_basin — AKMC skips the superbasin step and uses ordinary single-state KMC for that iteration

Configuration is under the [amsel] INI section (discover_decide, e_min_*, cv_threshold).

Configuration

[Coarse Graining]

References

[CG_Nov01]

M. A. Novotny. A Tutorial on Advanced Dynamic Monte Carlo Methods for Systems with Discrete State Spaces, pages 153–210. WORLD SCIENTIFIC, April 2001. doi:10.1142/9789812811578_0003.

[CG_Vot97]

Arthur F. Voter. Hyperdynamics: Accelerated Molecular Dynamics of Infrequent Events. Physical Review Letters, 78(20):3908–3911, May 1997. doi:10.1103/PhysRevLett.78.3908.