Carlo Jaeger, Stefan Klus, Christof Schütte, Sarah Wolf
Jan-Hendrik Niemann (ZIB)
01.01.2019 – 31.12.2021
Agent-based models (ABMs) describing the socio-economic behavior of entire populations are inherently high-dimensional. This project addresses the question whether it is possible to learn significantly reduced dynamical systems from simulation data.
It starts out from the Mobility Transition Model (MoTMo, developed by the Global Climate Forum), a spatially explicit large-scale parallel stochastic discrete-time ABM that simulates the evolution of private mobility demand in a socio-technical context. A synthetic population of up to millions of agents statistically reproduces distributions of age, gender, household size, income and population density to represent Germany. Agents take mobility decisions based on experience and information from their friendship networks, aiming to maximize individual objectives. The model has been parametrized to match extensive statistical data like vehicle distribution and individual mobility preferences. It is used in Decision Theatre workshops for model-stakeholder interactions, where stakeholders can experiment with different scenarios and their feedback can help improve the model. In such events, response time for making model changes is short and there is a need for reduced models of large-scale ABMs that can be learned directly from data.
The mathematical challenge is to obtain interpretable representations of the dynamics from a rather small number of measurements and then to extract further information from these representations, e.g., stationary distributions and almost invariant sets in state space. As a first step, a continuous-time stochastic agent-based model with simpler dynamics has been reformulated as a Markov jump process and its approximation by ordinary and stochastic differential equations (ODEs and SDEs, respectively) have been described (see Winkelmann et al., 2020).
Work in progress shows how coarse-grained models for agent-based dynamics can be learned from data using the Koopman generator, combining the results by Klus et al (2019) with the above. Exploiting assumptions about the highest order transition occurring in the agent-based model allows to limit the set of basis functions needed for system identification.
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