Verifying the robustness of using parameter space estimation with ridge regression to predict a critical transition

In this study, we verify the robustness of using parameter space estimation with ridge regression to predict a critical transition. The parameter space can be estimated from only two time-series data sets generated by a system with different parameter values. Thereby, we can predict the parameter value at which the critical transition will occur by plotting a bifurcation diagram in the estimated parameter space. We are able to show that this method can predict the critical transition from time-series data sets perturbed by several noise intensities. In numerical experiments, we verify the robustness for several noise intensities while adjusting a normalization parameter of the ridge regression. Additionally, we confirm the differences in the trained synaptic weights between when the predictions are successful and when we are unable to consistently obtain a successful prediction.