Fig. 5: Learning the stochastic transitions from the experimental data of protein folding.
From: Learning noise-induced transitions by multi-scaling reservoir computing
The u1 represents the end-to-end length of the protein. We refer to transitions from around u1 = 15 to around u1 = 30 as upward transitions, and vice versa as downward transitions. The right-pointing arrow: reduction of training data. a Time series of the training set (0 − 25000 time steps). b The trained slow-scale model generates slowly time-scale series (color lines), and the noise distribution is separated out. c The prediction during time steps 25000−50,000. d, e Histograms of upward and downward transition time for the prediction and the test data, where the length of the training set (Ttrain) is 25,000 time steps. Transition time refers to the interval between two consecutive transitions. f–i Similar histograms of upward and downward transition time with different lengths of the training sets, Ttrain = 7500 for (f, g), and Ttrain = 6000 for (h, i). The present method can still be accurate even when the training length is reduced to Ttrain = 7500.
