Tasks Makyth Models: Machine Learning Assisted Surrogates for Tipping Points

TL;DR

This paper introduces a machine learning framework that combines manifold learning, neural networks, and Gaussian processes to detect tipping points and predict rare catastrophic events in complex systems, demonstrated on a financial market agent-based model.

Contribution

It develops a novel ML-assisted multiscale modeling approach for identifying tipping points and characterizing rare events in high-dimensional complex systems.

Findings

Successfully constructed reduced-order models from high-dimensional data.

Effectively detected tipping points in the financial market model.

Characterized probabilities of catastrophic shifts near tipping points.

Abstract

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.