Global and local reduced models for interacting, heterogeneous agents.

Area of Science:

• Complex Systems Science
• Computational Neuroscience
• Data-Driven Modeling

Background:

• Simulating large, coupled, heterogeneous agent systems is computationally challenging due to complex emergent dynamics.
• Low-dimensional manifolds may govern the collective behavior of such systems, allowing for simplified surrogate models.
• Analytical identification of these simplified models is often intractable.

Purpose of the Study:

• To present a data-driven coarse-graining methodology for discovering reduced surrogate models from agent-based systems.
• To develop both globally based (ODE) and locally based (PDE) reduced models.
• To demonstrate the efficacy of these methods using a coupled neuron model.

Main Methods:

• Proper Orthogonal Decomposition (POD) to identify the low-dimensional dynamics manifold.
• Development of globally based models using POD coordinates to learn ordinary differential equations (ODEs).
• Development of locally based models learning partial differential equations (PDEs) in heterogeneity space, utilizing artificial neural network integrators (ResNet-templated).

Main Results:

• Learned reduced models (ODEs and PDEs) directly from agent-based system time series data.
• Demonstrated that both globally and locally coupled surrogate models can accurately reproduce complex dynamics.
• Validated the methodology on a simplified coupled neuron model exhibiting rhythmic oscillations.

Conclusions:

• Data-driven coarse-graining effectively discovers simplified surrogate models for complex agent-based systems.
• The methodology yields accurate ODEs (global) or PDEs (local) representing system dynamics on a low-dimensional manifold.
• Both all-to-all coupled and locally coupled reduced models can achieve comparable predictive performance.