Model-free and data-driven prediction of tipping point transitions in nonlinear dynamical systems is a challenging and outstanding task in complex systems science. We propose a novel, fully data-driven machine learning algorithm based on next-generation reservoir computing to extrapolate the bifurcation behavior of nonlinear dynamical systems using stationary training data samples. We show that this method can extrapolate tipping point transitions. Furthermore, it is demonstrated that the trained next-generation reservoir computing architecture can be used to predict non-stationary dynamics with time-varying bifurcation parameters. In doing so, post-tipping point dynamics of unseen parameter regions can be simulated.

翻译：在非线性动力系统中，无模型且数据驱动的临界转变点预测是复杂系统科学中一项具有挑战性的重要任务。我们提出了一种基于下一代储层计算的全新全数据驱动机器学习算法，利用平稳训练数据样本外推非线性动力系统的分岔行为。研究表明，该方法能够外推临界转变点。此外，实验证明，训练后的下一代储层计算架构可用于预测具有时变分岔参数的非平稳动力学过程。由此，可模拟未见参数区域中临界转变后的动力学行为。