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; Ioannis G Kevrekidis

doi:10.1038/s41467-024-48024-7

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

Nat Commun. 2024 May 15;15(1):4117. doi: 10.1038/s41467-024-48024-7.

Authors

Gianluca Fabiani^{1

2}, Nikolaos Evangelou², Tianqi Cui², Juan M Bello-Rivas³, Cristina P Martin-Linares⁴, Constantinos Siettos⁵, Ioannis G Kevrekidis^{6

7

8}

Affiliations

¹ Modelling Engineering Risk and Complexity, Scuola Superiore Meridionale, Naples, Italy.
² Department of Chemical and Biomolecular Engineering, Johns Hopkins University, Baltimore, MD, USA.
³ Department of Applied Mathematics and Statistics, Johns Hopkins University, Baltimore, MD, USA.
⁴ Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD, USA.
⁵ Dipartimento di Matematica e Applicazioni 'Renato Caccioppoli', Università degli Studi di Napoli Federico II, Naples, Italy. constantinos.siettos@unina.it.
⁶ Department of Chemical and Biomolecular Engineering, Johns Hopkins University, Baltimore, MD, USA. yannisk@jhu.edu.
⁷ Department of Applied Mathematics and Statistics, Johns Hopkins University, Baltimore, MD, USA. yannisk@jhu.edu.
⁸ School of Medicine's Dept. of Urology, Johns Hopkins University, Baltimore, MD, USA. yannisk@jhu.edu.

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.