Fig. 2: Capturing stochastic transitions in a bistable gradient system with white noise.
From: Learning noise-induced transitions by multi-scaling reservoir computing
a Schematic of noise-induced transitions in the bistable gradient system with Gaussian white noise. b Generated time series from Eq. (9) (b = 5, c = 0, ε = 0.3, u1(0) = 1.5, δt = 0.01) with t = 30 as the ground truth. c The trained slow-scale model transforms ten different start points into ten different slowly time-scale series (color lines), and the noise distribution is separated. d The prediction for t ∈ [100, 130]. e The number of transitions for the test and predicted data matches. Transition refers to the shift from u1 = − 1 to u1 = 1 or vice versa. The duration of the prediction is 10000δt. f Histograms of transition time for the test and predicted data. Transition time refers to the interval between two consecutive transitions.
