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Ordered Line Integral Methods for Computing the Quasi-potential. (arXiv:1706.07509v1 [math.NA])
来源于:arXiv
The quasi-potential is a key function in the Large Deviation Theory. It
characterizes the difficulty of the escape from the neighborhood of an
attractor of a stochastic non-gradient dynamical system due to the influence of
small white noise. It also gives an estimate of the invariant probability
distribution in the neighborhood of the attractor up to the exponential order.
We present a new family of methods for computing the quasi-potential on a
regular mesh named the Ordered Line Integral Methods (OLIMs). In comparison
with the first proposed quasi-potential finder based on the Ordered Upwind
Method (OUM) (Cameron, 2012), the new methods are 1.5 to 3.5 times faster, can
produce error about two orders of magnitude smaller, and may exhibit faster
convergence. Similar to the OUM, OLIMs employ the dynamical programming
principle. Contrary to it, they (i) have an optimized strategy for the use of
computationally expensive triangle updates leading to a notable speed-up, and
(ii) directly so 查看全文>>