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

Area of Science:

• Computational Science
• Complex Systems Modeling
• Machine Learning

Background:

• Agent-based simulators generate complex dynamics, making analysis computationally intensive.
• Identifying tipping points and quantifying rare event uncertainty are crucial for risk assessment in various systems.

Purpose of the Study:

• To develop a machine learning framework for constructing effective reduced order models (ROMs).
• To enable systematic multiscale numerical analysis of emergent dynamics, focusing on tipping point detection and rare event uncertainty quantification.

Main Methods:

• Integration of manifold learning, neural networks, Gaussian processes, and an Equation-Free multiscale approach.
• Application to an event-driven stochastic financial market model and a stochastic epidemic model on an Erdös-Rényi network.

Main Results:

• The framework successfully constructs ROMs from detailed agent-based simulators.
• Emergent dynamics near tipping points were found to be describable by a one-dimensional stochastic differential equation, revealing intrinsic dimensionality.
• Computational cost for analysis tasks was significantly reduced.

Conclusions:

• The proposed machine learning framework offers an efficient approach for analyzing complex system dynamics.
• The identified intrinsic dimensionality simplifies the analysis of tipping points and rare events.
• This method provides a powerful tool for understanding and predicting critical transitions in stochastic systems.