Reconstruction of Bifurcation Diagrams Using Extreme Learning Machines

We describe a method for reconstructing bifurcation diagrams by using extreme learning machines (ELM). Principal component analysis (PCA) is performed for the coefficient vector obtained by training the time-series predictor. From the results of PCA, we estimate the number of significant parameters of the target system, reconstruct the bifurcation diagram, and compare it with the original one. The results show that the computation time required by ELM is considerably shorter than that required by conventional methods. In addition, we quantitatively evaluate the accuracy of reconstruction of bifurcation diagrams using a structural similarity extraction method based on fractal image compression.