Active search for Bifurcations

TL;DR

This paper introduces an active learning approach using Bayesian Optimization to efficiently locate bifurcations in complex, noisy dynamical systems with limited data, aiding understanding and intervention planning.

Contribution

It presents a novel active learning framework that leverages Bayesian Optimization to identify bifurcations with minimal observations in resource-constrained settings.

Findings

Effective in noisy, complex systems

Reduces number of required observations

Provides uncertainty quantification

Abstract

Bifurcations mark qualitative changes of long-term behavior in dynamical systems and can often signal sudden ("hard") transitions or catastrophic events (divergences). Accurately locating them is critical not just for deeper understanding of observed dynamic behavior, but also for designing efficient interventions. When the dynamical system at hand is complex, possibly noisy, and expensive to sample, standard (e.g. continuation based) numerical methods may become impractical. We propose an active learning framework, where Bayesian Optimization is leveraged to discover saddle-node or Hopf bifurcations, from a judiciously chosen small number of vector field observations. Such an approach becomes especially attractive in systems whose state x parameter space exploration is resource-limited. It also naturally provides a framework for uncertainty quantification (aleatoric and epistemic), useful in systems with inherent stochasticity.