Task-oriented machine learning surrogates for tipping points of agent-based models

Gianluca Fabiani, Nikolaos Evangelou, Tianqi Cui, Juan M. Bello-Rivas, Cristina P. Martin-Linares, Constantinos Siettos () and Ioannis G. Kevrekidis ()
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Gianluca Fabiani: Scuola Superiore Meridionale
Nikolaos Evangelou: Johns Hopkins University
Tianqi Cui: Johns Hopkins University
Juan M. Bello-Rivas: Johns Hopkins University
Cristina P. Martin-Linares: Johns Hopkins University
Constantinos Siettos: Università degli Studi di Napoli Federico II
Ioannis G. Kevrekidis: Johns Hopkins University

Nature Communications, 2024, vol. 15, issue 1, 1-13

Abstract: Abstract We present a machine learning framework bridging manifold learning, neural networks, Gaussian processes, and Equation-Free multiscale approach, for the construction of different types of effective reduced order models from detailed agent-based simulators and the systematic multiscale numerical analysis of their emergent dynamics. The specific tasks of interest here include the detection of tipping points, and the uncertainty quantification of rare events near them. Our illustrative examples are an event-driven, stochastic financial market model describing the mimetic behavior of traders, and a compartmental stochastic epidemic model on an Erdös-Rényi network. We contrast the pros and cons of the different types of surrogate models and the effort involved in learning them. Importantly, the proposed framework reveals that, around the tipping points, the emergent dynamics of both benchmark examples can be effectively described by a one-dimensional stochastic differential equation, thus revealing the intrinsic dimensionality of the normal form of the specific type of the tipping point. This allows a significant reduction in the computational cost of the tasks of interest.

Date: 2024
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DOI: 10.1038/s41467-024-48024-7

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