# Active search for Bifurcations

arXiv: https://arxiv.org/abs/2406.11141 · HTML: https://mlsanity.com/paper/2406.11141/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 84 references that are in the map.
- First posted on arXiv 17 Jun 2024.

## Builds on (most cited first, 17 of 17)

- [Coarse-scale PDEs from fine-scale observations via machine learning](https://mlsanity.com/paper/1909.05707/) (2019)
- [Discovering and forecasting extreme events via active learning in neural operators](https://mlsanity.com/paper/2204.02488/) (2022)
- [Active Learning for Optimal Intervention Design in Causal Models](https://mlsanity.com/paper/2209.04744/) (2022)
- [Scaling Gaussian Process Regression with Derivatives](https://mlsanity.com/paper/1810.12283/) (2018)
- [Constructing coarse-scale bifurcation diagrams from spatio-temporal observations of microscopic simulations: A parsimonious machine learning approach](https://mlsanity.com/paper/2201.13323/) (2022)
- [Probabilistic ODE Solvers with Runge-Kutta Means](https://mlsanity.com/paper/1406.2582/) (2014)
- [Bayesian ODE Solvers: The Maximum A Posteriori Estimate](https://mlsanity.com/paper/2004.00623/) (2020)
- [Learning black- and gray-box chemotactic PDEs/closures from agent based Monte Carlo simulation data](https://mlsanity.com/paper/2205.13545/) (2022)
- [Bayesian System ID: Optimal management of parameter, model, and measurement uncertainty](https://mlsanity.com/paper/2003.02359/) (2020)
- [A sequential sampling strategy for extreme event statistics in nonlinear dynamical systems](https://mlsanity.com/paper/1804.07240/) (2018)
- [Output-weighted optimal sampling for Bayesian regression and rare event statistics using few samples](https://mlsanity.com/paper/1907.07552/) (2019)
- [Nonlinear dimensionality reduction then and now: AIMs for dissipative PDEs in the ML era](https://mlsanity.com/paper/2310.15816/) (2023)
- [Output-Weighted Sampling for Multi-Armed Bandits with Extreme Payoffs](https://mlsanity.com/paper/2102.10085/) (2021)
- [Using scientific machine learning for experimental bifurcation analysis of dynamic systems](https://mlsanity.com/paper/2110.11854/) (2021)
- [Limits of Entrainment of Circadian Neuronal Networks](https://mlsanity.com/paper/2208.11119/) (2022)
- [Modelling of physical systems with a Hopf bifurcation using mechanistic models and machine learning](https://mlsanity.com/paper/2209.06910/) (2022)
- [Evaluation of machine learning architectures on the quantification of epistemic and aleatoric uncertainties in complex dynamical systems](https://mlsanity.com/paper/2306.15159/) (2023)

## Built on by (most cited first, 2 of 2)

- [Multimodal Scientific Learning Beyond Diffusions and Flows](https://mlsanity.com/paper/2602.00960/) (2026)
- [On Some Tunable Multi-fidelity Bayesian Optimization Frameworks](https://mlsanity.com/paper/2508.01013/) (2025)

## Abstract (arXiv)

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.