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 spatiotemporal 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 while retaining the inherent model stochasticity. 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.

自然地，许多现实过程都可以建模为交互代理系统。但是，当系统变得太大时，这种基于代理的模型的长期仿真通常很棘手。在本文中，从基于随机时空代理的模型（ABM）开始，我们提出了一种基于随机PDE的简化模型，该模型描述了大型种群的代理数量密度的演变，同时保留了固有的模型随机性。我们讨论两种方法的算法细节。关于SPDE模型，我们在空间中应用有限元离散化，这不仅可以确保有效的仿真，而且可以作为SPDE的正则化。给出了在代理之间传播创新的说明性示例，并将其用于比较ABM和SPDE模型。