A new simplified ordered upwind method for calculating quasi-potential

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 concernin 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.