Bifurcation diagrams in estimated parameter space using a pruned extreme learning machine

Abstract

We propose an algorithm to estimate parameter spaces by using a pruned extreme learning machine, but without using principal component analysis, and we plot bifurcation diagrams in the estimated parameter spaces to visualize changes in system patterns. The estimation of parameter spaces can predict changes in the behavior of a system when its parameters are changed. It can be very helpful to adjust the optimal parameters of unknown systems. In this paper, we estimate the dimension of parameter spaces using the singular values of trained synaptic weights and the parameter spaces based on the method proposed by Bagarinao etal., using a pruned extreme learning machine. We motivate this use of a pruned extreme learning machine through numerical experiments, with the estimation of the dimension of parameter spaces for various systems, and we show that the proposed method can successfully plot bifurcation diagrams in the estimated parameter spaces. In addition, we show the results of a bifurcation diagram in the estimated parameter space for maps that are nonlinear-in-parameters, since Bagarinao etal. limited their method to linear-in-parameters maps. In particular, we estimate the parameter spaces for a mathematical model of induction motor drives and for a model of vegetation biomass in ecosystems, which are both nonlinear-in-parameter maps corresponding to real-world systems.