SINDy meets Schelling. Transforming Agent-Based model spatial outputs into Dynamical Systems

Agent-based models (ABMs) are standard tools for modeling social and physical phenomena from the ground up by building detailed simulations in which individual agents interact and study emergent behavior. However, since they are simulations, it is challenging to generalize or even quantitatively interpret the results. A frequent output of an ABM model is a grid with points of one or more classes that represent the agents’ configuration over time. A canonical example is the Schelling segregation model, where agents of two types follow a simple relocation rule based on their tolerance to the proportion of different agents in a given location, resulting in a segregated configuration that is visually revealing but not quantitative. In this work, we propose assigning a quantitative measure of entropy, based on the spatial configuration of the steady state of the Schelling model, to a range of population values in the model using Topological Data Analysis (TDA) techniques. The resulting dataset of quantitative metrics related to the original configuration is analyzed via Sparse Identification of Nonlinear Dynamics (SINDy) methods to obtain a representation of the system dynamics in the form of an ordinary differential equation.