From interacting agents to density-based modeling with stochastic PDEs

Abstract

Many real-world processes can naturally be modeled as systems of interacting agents. However, the long-term simulation of such agent-based models is often intractable when the system becomes too large. In this paper, starting from a stochastic spatio-temporal agent-based model (ABM), we present a reduced model in terms of stochastic PDEs that describes the evolution of agent number densities for large populations. We discuss the algorithmic details of both approaches; regarding the SPDE model, we apply Finite Element discretization in space which not only ensures efficient simulation but also serves as a regularization of the SPDE. Illustrative examples for the spreading of an innovation among agents are given and used for comparing ABM and SPDE models.

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• Field theories and quantum methods for stochastic reaction-diffusion systems
• Co-evolving networks for opinion and social dynamics in agent-based models
• A Hybrid ABM-PDE Framework for Real-World Infectious Disease Simulations
• Machine Learning for the identification of phase-transitions in interacting agent-based systems: a Desai-Zwanzig example
• Mean field limits of particle-based stochastic reaction-drift-diffusion models
• A Hybrid Algorithm for Systems of Non-interacting Particles with an External Potential