From interacting agents to density-based modeling with stochastic PDEs

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