Data-driven control of agent-based models: An Equation/Variable-free machine learning approach

We present an Equation/Variable free machine learning (EVFML) framework for the control of collective dynamics complex/multiscale systems modelled via microscopic/agent-based simulators. The approach obviates need construction surrogate, reduced-order models.~The proposed implementation consists three steps: (A) from high-dimensional agent-based simulations, (in particular, non-linear manifold (Diffusion Maps (DMs)) helps identify a set coarse-grained variables that parametrize low-dimensional on which emergent/collective evolve. out-of-sample extension and pre-image problems, i.e. mappings input space to back, are solved by coupling DMs with Nystrom Geometric Harmonics, respectively; (B) having identified its coordinates, we exploit Equation-free perform numerical bifurcation analysis emergent dynamics; then (C) based previous steps, design data-driven embedded wash-out controllers drive simulators their intrinsic, imprecisely known, open-loop unstable steady-states, thus demonstrating scheme is robust against approximation errors modelling uncertainty.~The efficiency illustrated controlling (i) traveling waves deterministic model traffic dynamics, (ii) equilibria stochastic financial market agent mimesis.