2020/12/31 by Jan-Hendrik Niemann, Stefan Klus, Christof Schütte
Computer Science · Mathematics · Physics and Astronomy · #Benchmark (surveying) #Computational Physics and Python Applications #Computer science #Differential equation #Dynamical systems theory #Gaussian Processes and Bayesian Inference #Generator (circuit theory) #Mathematical optimization #Mathematics #Model Reduction and Neural Networks #Operator (biology) #Ordinary differential equation #Physics #Population #Power (physics) #Reduction (mathematics) #math.DS #stat.ML
paper · pdf · doi:10.1371/journal.pone.0250970
arxiv created 2021/05/11 · openalex publication_date 2021/05/13 · arxiv updated 2022/01/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
The dynamical behavior of social systems can be described by agent-based models. Although single agents follow easily explainable rules, complex time-evolving patterns emerge due to their interaction. The simulation and analysis of such agent-based models, however, is often prohibitively time-consuming if the number of agents is large. In this paper, we show how Koopman operator theory can be used to derive reduced models of agent-based systems using only simulation data. Our goal is to learn coarse-grained models and to represent the reduced dynamics by ordinary or stochastic differential equations. The new variables are, for instance, aggregated state variables of the agent-based model, modeling the collective behavior of larger groups or the entire population. Using benchmark problems with known coarse-grained models, we demonstrate that the obtained reduced systems are in good agreement with the analytical results, provided that the numbers of agents is sufficiently large.