Tasks Makyth Models: Machine Learning Assisted Surrogates for Tipping Points

• URL: http://arxiv.org/abs/2309.14334v1
• Date: Mon, 25 Sep 2023 17:58:23 GMT
• Title: Tasks Makyth Models: Machine Learning Assisted Surrogates for Tipping Points
• Authors: Gianluca Fabiani, Nikolaos Evangelou, Tianqi Cui, Juan M. Bello-Rivas, Cristina P. Martin-Linares, Constantinos Siettos, Ioannis G. Kevrekidis
• Abstract summary: We present a machine learning (ML)-assisted framework for detecting tipping points in the emergent behavior of complex systems. We construct reduced-order models for the emergent dynamics at different scales. We contrast the uses of the different models and the effort involved in learning them.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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