Active search for Bifurcations
This addresses the challenge of efficiently identifying critical transitions in resource-limited dynamical systems, such as those in engineering or biology, though it is an incremental application of existing methods to a specific domain.
The paper tackled the problem of locating bifurcations in complex, noisy, and expensive-to-sample dynamical systems by proposing an active learning framework using Bayesian Optimization, which efficiently discovers saddle-node or Hopf bifurcations with a small number of vector field observations and provides uncertainty quantification.
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.