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Tasks Makyth Models: Machine Learning Assisted Surrogates for Tipping Points

Author

Listed:
  • Gianluca Fabiani
  • Nikolaos Evangelou
  • Tianqi Cui
  • Juan M. Bello-Rivas
  • Cristina P. Martin-Linares
  • Constantinos Siettos
  • Ioannis G. Kevrekidis

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.

Suggested Citation

  • Gianluca Fabiani & Nikolaos Evangelou & Tianqi Cui & Juan M. Bello-Rivas & Cristina P. Martin-Linares & Constantinos Siettos & Ioannis G. Kevrekidis, 2023. "Tasks Makyth Models: Machine Learning Assisted Surrogates for Tipping Points," Papers 2309.14334, arXiv.org.
    • Handle: RePEc:arx:papers:2309.14334
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    References listed on IDEAS

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    1. Marten Scheffer, 2010. "Foreseeing tipping points," Nature, Nature, vol. 467(7314), pages 411-412, September.
    2. Siettos, Constantinos, 2014. "Coarse-grained computational stability analysis and acceleration of the collective dynamics of a Monte Carlo simulation of bacterial locomotion," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 836-847.
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