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

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