We present a machine learning (ML)-assisted framework bridging manifold learning, neural networks, Gaussian processes, and Equation-Free multiscale modeling, for (a) detecting tipping points in the emergent behavior of complex systems, and (b) characterizing probabilities of rare events (here, catastrophic shifts) near them. Our illustrative example is an event-driven, stochastic agent-based model (ABM) describing the mimetic behavior of traders in a simple financial market. Given high-dimensional spatiotemporal data -- generated by the stochastic ABM -- we construct reduced-order models for the emergent dynamics at different scales: (a) mesoscopic Integro-Partial Differential Equations (IPDEs); and (b) mean-field-type Stochastic Differential Equations (SDEs) embedded in a low-dimensional latent space, targeted to the neighborhood of the tipping point. We contrast the uses of the different models and the effort involved in learning them.

翻译：我们提出了一种机器学习（ML）辅助框架，该框架结合了流形学习、神经网络、高斯过程和免方程多尺度建模，用于（a）检测复杂系统涌现行为中的临界转变点，以及（b）表征其附近罕见事件（此处为灾难性转变）的概率。我们的示例是一个事件驱动的随机基于代理模型（ABM），用于描述简单金融市场中交易者的模仿行为。基于该随机ABM生成的高维时空数据，我们构建了不同尺度上涌现动态的降阶模型：（a）介观积分-偏微分方程（IPDEs）；（b）嵌入低维潜在空间中的平均场型随机微分方程（SDEs），并聚焦于临界转变点邻域。我们对比了不同模型的用途及其学习所需的工作量。