Volume 18, Issue 5
A Minimum Action Method with Optimal Linear Time Scaling

Commun. Comput. Phys., 18 (2015), pp. 1352-1379.

Published online: 2018-04

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In this work, we develop a minimum action method (MAM) with optimal linear time scaling, called tMAM for short. The main idea is to relax the integration time as a functional of the transition path through optimal linear time scaling such that a direct optimization of the integration time is not required. The Feidlin-Wentzell action functional is discretized by finite elements, based on which h-type adaptivity is introduced to tMAM. The adaptive tMAM does not require reparametrization for the transition path. It can be applied to dealing with quasi-potential: 1) When the minimal action path is subject to an infinite integration time due to critical points, tMAM with a uniform mesh converges algebraically at a lower rate than the optimal one. However, the adaptive tMAM can recover the optimal convergence rate. 2) When the minimal action path is subject to a finite integration time, tMAM with a uniform mesh converges at the optimal rate since the problem is not singular, and the optimal integration time can be obtained directly from the minimal action path. Numerical experiments have been implemented for both SODE and SPDE examples.

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@Article{CiCP-18-1352, author = {}, title = {A Minimum Action Method with Optimal Linear Time Scaling}, journal = {Communications in Computational Physics}, year = {2018}, volume = {18}, number = {5}, pages = {1352--1379}, abstract = {

In this work, we develop a minimum action method (MAM) with optimal linear time scaling, called tMAM for short. The main idea is to relax the integration time as a functional of the transition path through optimal linear time scaling such that a direct optimization of the integration time is not required. The Feidlin-Wentzell action functional is discretized by finite elements, based on which h-type adaptivity is introduced to tMAM. The adaptive tMAM does not require reparametrization for the transition path. It can be applied to dealing with quasi-potential: 1) When the minimal action path is subject to an infinite integration time due to critical points, tMAM with a uniform mesh converges algebraically at a lower rate than the optimal one. However, the adaptive tMAM can recover the optimal convergence rate. 2) When the minimal action path is subject to a finite integration time, tMAM with a uniform mesh converges at the optimal rate since the problem is not singular, and the optimal integration time can be obtained directly from the minimal action path. Numerical experiments have been implemented for both SODE and SPDE examples.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.030614.180315a}, url = {http://global-sci.org/intro/article_detail/cicp/11072.html} }
TY - JOUR T1 - A Minimum Action Method with Optimal Linear Time Scaling JO - Communications in Computational Physics VL - 5 SP - 1352 EP - 1379 PY - 2018 DA - 2018/04 SN - 18 DO - http://doi.org/10.4208/cicp.030614.180315a UR - https://global-sci.org/intro/article_detail/cicp/11072.html KW - AB -

In this work, we develop a minimum action method (MAM) with optimal linear time scaling, called tMAM for short. The main idea is to relax the integration time as a functional of the transition path through optimal linear time scaling such that a direct optimization of the integration time is not required. The Feidlin-Wentzell action functional is discretized by finite elements, based on which h-type adaptivity is introduced to tMAM. The adaptive tMAM does not require reparametrization for the transition path. It can be applied to dealing with quasi-potential: 1) When the minimal action path is subject to an infinite integration time due to critical points, tMAM with a uniform mesh converges algebraically at a lower rate than the optimal one. However, the adaptive tMAM can recover the optimal convergence rate. 2) When the minimal action path is subject to a finite integration time, tMAM with a uniform mesh converges at the optimal rate since the problem is not singular, and the optimal integration time can be obtained directly from the minimal action path. Numerical experiments have been implemented for both SODE and SPDE examples.

Xiaoliang Wan. (2020). A Minimum Action Method with Optimal Linear Time Scaling. Communications in Computational Physics. 18 (5). 1352-1379. doi:10.4208/cicp.030614.180315a
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