A new simplified ordered upwind method for calculating quasi-potential

doi:10.1088/1674-1056/ac140f

中国物理B ›› 2022, Vol. 31 ›› Issue (1): 10502-010502.doi: 10.1088/1674-1056/ac140f

A new simplified ordered upwind method for calculating quasi-potential

Qing Yu(虞晴) and Xianbin Liu(刘先斌)^†

State Key Laboratory of Mechanics and Control for Mechanical Structures, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

收稿日期:2021-05-30 修回日期:2021-06-30 接受日期:2021-07-14 出版日期:2021-12-03 发布日期:2021-12-14
通讯作者: Xianbin Liu E-mail:xbliu@nuaa.edu.cn
基金资助:
This work was supported by the National Natural Science Foundation of China (Grant Nos. 11772149 and 12172167), the Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD), and the Research Fund of State Key Laboratory of Mechanics and Control of Mechanical Structures (Grant No. MCMS-I-19G01).

A new simplified ordered upwind method for calculating quasi-potential

Qing Yu(虞晴) and Xianbin Liu(刘先斌)^†

State Key Laboratory of Mechanics and Control for Mechanical Structures, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

Received:2021-05-30 Revised:2021-06-30 Accepted:2021-07-14 Online:2021-12-03 Published:2021-12-14
Contact: Xianbin Liu E-mail:xbliu@nuaa.edu.cn
Supported by:
This work was supported by the National Natural Science Foundation of China (Grant Nos. 11772149 and 12172167), the Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD), and the Research Fund of State Key Laboratory of Mechanics and Control of Mechanical Structures (Grant No. MCMS-I-19G01).

摘要/Abstract

摘要： We present a new method for calculation of quasi-potential, which is a key concept in the large deviation theory. This method adopts the "ordered" idea in the ordered upwind algorithm and different from the finite difference upwind scheme, the first-order line integral is used as its update rule. With sufficient accuracy, the new simplified method can greatly speed up the computational time. Once the quasi-potential has been computed, the minimum action path (MAP) can also be obtained. Since the MAP is of concern in most stochastic situations, the effectiveness of this new method is checked by analyzing the accuracy of the MAP. Two cases of isotropic diffusion and anisotropic diffusion are considered. It is found that this new method can both effectively compute the MAPs for systems with isotropic diffusion and reduce the computational time. Meanwhile anisotropy will affect the accuracy of the computed MAP.

关键词: quasi-potential, ordered upwind algorithm, minimum action path, isotropic diffusion and anisotropic diffusion

Abstract: We present a new method for calculation of quasi-potential, which is a key concept in the large deviation theory. This method adopts the "ordered" idea in the ordered upwind algorithm and different from the finite difference upwind scheme, the first-order line integral is used as its update rule. With sufficient accuracy, the new simplified method can greatly speed up the computational time. Once the quasi-potential has been computed, the minimum action path (MAP) can also be obtained. Since the MAP is of concern in most stochastic situations, the effectiveness of this new method is checked by analyzing the accuracy of the MAP. Two cases of isotropic diffusion and anisotropic diffusion are considered. It is found that this new method can both effectively compute the MAPs for systems with isotropic diffusion and reduce the computational time. Meanwhile anisotropy will affect the accuracy of the computed MAP.

Key words: quasi-potential, ordered upwind algorithm, minimum action path, isotropic diffusion and anisotropic diffusion

中图分类号: (Fluctuation phenomena, random processes, noise, and Brownian motion)

05.40.-a

05.45.-a (Nonlinear dynamics and chaos) 05.40.Ca (Noise)

Qing Yu(虞晴) and Xianbin Liu(刘先斌). A new simplified ordered upwind method for calculating quasi-potential[J]. 中国物理B, 2022, 31(1): 10502-010502.

Qing Yu(虞晴) and Xianbin Liu(刘先斌). A new simplified ordered upwind method for calculating quasi-potential[J]. Chin. Phys. B, 2022, 31(1): 10502-010502.

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A new simplified ordered upwind method for calculating quasi-potential

A new simplified ordered upwind method for calculating quasi-potential

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