Agent-based simulations provide accurate and detailed insights into dynamical systems. However, the run-times and computational burden of these microscopic simulations often prohibit large-scale parameter studies or overviews on coarser scales. These tasks can be done with coarser models, but those often suffer from low accuracy compared to the agent-based approach. As a remedy, this project aims to learn coarse models directly from the agent-based data. We identify effective stochastic differential equations (SDE) for coarse observables of fine-grained particle- or agent-based simulations. These SDE then provide coarse surrogate models of the fine scale dynamics. The coarse variables in question for this project are the infection states for a viral disease that is spreading through a local population. The crowd simulation software Vadere will be used for the agent-based modelling and simulation, all necessary software implementations are already available, but can be extended and tailored to our needs. To learn the SDE, we approximate the drift and diffusivity functions of the effective SDE through neural networks, which can be thought of as effective stochastic ResNets. The loss function is inspired by the structure of established stochastic numerical integrators, namely the Euler-Maruyama integrator. Our approximations can thus benefit from error analysis of these underlying numerical schemes. They also lend themselves naturally to ”physics-informed” gray-box identification when approximate coarse models, such as mean field equations, are available. The learning procedure we use does not require long trajectories, works on scattered snapshot data, and is designed to naturally handle different time steps per snapshot.     «

Agent-based simulations provide accurate and detailed insights into dynamical systems. However, the run-times and computational burden of these microscopic simulations often prohibit large-scale parameter studies or overviews on coarser scales. These tasks can be done with coarser models, but those often suffer from low accuracy compared to the agent-based approach. As a remedy, this project aims to learn coarse models directly from the agent-based data. We identify effective stochastic differen...     »