Tasks Makyth Models: Machine Learning Assisted Surrogates for Tipping Points
This work addresses the challenge of predicting catastrophic shifts in complex systems like financial markets, offering a novel computational approach that is incremental in combining existing techniques for improved modeling.
The paper tackled the problem of detecting tipping points and characterizing rare event probabilities in complex systems, such as financial markets, by developing a machine learning-assisted framework that integrates manifold learning, neural networks, and Gaussian processes, resulting in reduced-order models like IPDEs and SDEs for efficient analysis.
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.