6 papers · 1 filter
DeepWKB: Learning WKB Expansions of Invariant Distributions for Stochastic Systems
Yao Li, Yicheng Liu, Shirou Wang
This paper introduces a novel deep learning method, called DeepWKB, for estimating the invariant distribution of randomly perturbed systems via its Wentzel-Kramers-Brillouin (WKB)…
Entropy formula of folding type for maps
Gang Liao, Shirou Wang
In the study of non-equilibrium statistical mechanics, Ruelle derived explicit formulae for entropy production of smooth dynamical systems. The vanishing or strict positivity of en…
Numerical computations of geometric ergodicity for stochastic dynamics
Yao Li, Shirou Wang
A probabilistic approach of computing geometric rate of convergence of stochastic processes is introduced in this paper. The goal is to quantitatively compute both upper and lower…
Synchronization in discrete-time, discrete-state Random Dynamical Systems
Wen Huang, Hong Qian, Shirou Wang +2
We characterize synchronization phenomenon in discrete-time, discrete-state random dynamical systems, with random and probabilistic Boolean networks as particular examples. In term…
Continuity properties of folding entropy
Gang Liao, Shirou Wang
The folding entropy is a quantity originally proposed by Ruelle in 1996 during the study of entropy production in the non-equilibrium statistical mechanics. As derived through a li…
Measures of intermediate entropies for star vector fields
Ming Li, Yi Shi, Shirou Wang +1
We prove that all star vector fields, including Lorenz attractors and multisingular hyperbolic vector fields, admit the intermediate entropy property. To be precise, if is a st…