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Forward flux sampling-type schemes for simulating rare events: Efficiency analysis
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10.1063/1.2198827
/content/aip/journal/jcp/124/19/10.1063/1.2198827
http://aip.metastore.ingenta.com/content/aip/journal/jcp/124/19/10.1063/1.2198827

Figures

Image of FIG. 1.
FIG. 1.

Schematic illustration of the definition of regions and and the interfaces (Here, ). Three transition paths are shown.

Image of FIG. 2.
FIG. 2.

Cost for evenly spaced interfaces , , , , and . (a) as a function of for . (b) as a function of for .

Image of FIG. 3.
FIG. 3.

Relative variance , for , , and . The circles show the function . (a) as a function of for . (b) as a function of for .

Image of FIG. 4.
FIG. 4.

Relative variance in , as predicted by Eqs. (50)–(52), for the model problem of Figs. 2 and 3 with and . The upper curves in each group correspond to , the middle curves to , and the lower curves to . (a) as a function of , keeping . (b) as a function of , keeping .

Image of FIG. 5.
FIG. 5.

Efficiency , calculated using Eq. (4), for the simple model of Figs. 2–4. For each method, results are plotted with (lower curves) and (upper curves). (a) as a function of for . (b) as a function of for .

Image of FIG. 6.
FIG. 6.

Typical trajectory for a brute-force simulation of the Maier-Stein system, with , , and .

Image of FIG. 7.
FIG. 7.

Costs of trial runs between interfaces for the Maier-Stein system. The average lengths, in simulation steps, of “successful” trials (to ) are shown as filled circles. For these trials, and . The average lengths of “unsuccessful” trials (to ) are shown as open circles. For these trials, . The solid lines show the linear approximation [Eq. (6)], with .

Image of FIG. 8.
FIG. 8.

Predicted and measured values of for the Maier-Stein problem, as described in Sec. IV. The lines show the theoretical predictions for the FFS (solid line), BG (dotted line), and RB (dashed line) methods. The symbols show the simulation results. Circles: FFS method, squares: BG method, and triangles: RB method (with Metropolis acceptance/rejection). Simulation results were obtained with 400 blocks of starting points for FFS and 2000 starting points per block for BG and RB. (a) as a function of for . (b) as a function of for for evenly spaced interfaces.

Image of FIG. 9.
FIG. 9.

Predicted and measured values of for the Maier-Stein problem. The lines show the theoretical predictions for the FFS (solid line), BG (dotted line), and RB (dashed line) methods. The symbols show the simulation results. Circles: FFS method, squares: BG method, and triangles: RB method (with Metropolis acceptance/rejection). Simulation results were obtained with 400 blocks of starting points for FFS and 2000 starting points per block for BG and RB. Interfaces were evenly spaced between and . (a) as a function of for . (b) as a function of for . In (b), the landscape contribution is not included in the theoretical calculation.

Image of FIG. 10.
FIG. 10.

Predicted and measured values of for the Maier-Stein problem for the FFS method. Solid line: Eq. (50) (with the landscape variance), dotted line: Eq. (23) (no landscape variance), and circles: simulation results.

Image of FIG. 11.
FIG. 11.

Predicted and measured efficiency for the Maier-Stein system. The lines show the theoretical predictions for the FFS (solid line), BG (dotted line), and RB (dashed line) methods. The symbols show the simulation results. Circles: FFS method, squares: BG method, and triangles: RB method (with Metropolis acceptance/rejection). Simulation results were obtained with 400 blocks. For FFS, each block had starting points, and for BG and RB each blocks had 2000 starting points. Interfaces were evenly spaced. (a) vs for . (b) vs for . No landscape contribution to is included in panel b.

Image of FIG. 12.
FIG. 12.

(a) “Simulated” and predicted acceptance probabilities for interfaces for the “simulated simulation” described in the text, for . (b) Simulated and predicted values of for for the Maier-Stein problem of Sec. 4, for . In both plots, solid lines represent predicted values for , dotted lines, , and dashed lines, . Symbols represent simulation results: circles: , squares: , and triangles: .

Image of FIG. 13.
FIG. 13.

(solid line) and (dashed line), as functions of , calculated using FFS as described in Appendix D, for the Maier-Stein problem of Sec. IV with 10 000 points at the first interface .

Tables

Generic image for table
Table I.

Positions of the interfaces and measured values of and for the Maier-Stein problem.

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/content/aip/journal/jcp/124/19/10.1063/1.2198827
2006-05-19
2014-04-20
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Forward flux sampling-type schemes for simulating rare events: Efficiency analysis
http://aip.metastore.ingenta.com/content/aip/journal/jcp/124/19/10.1063/1.2198827
10.1063/1.2198827
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