Data-driven Control of Agent-based Models: an Equation/Variable-free Machine Learning Approach

For the task of identification of macroscopic variables from high-fidelity simulations/spatio-temporal data, various machine learning methods have been proposed including non-linear manifold learning algorithms such as Diffusion Maps (DMs) [5-13], ISOMAP [14-16] and Local Linear Embedding [17, 18] but also Autoencoders [19, 20]. For the task of the extraction of surrogate models for the approximation of the emergent dynamics, available approaches include the Sparse Identification of the Nonlinear Dynamics (SINDy) [21], the Koopman operator [22-27], Gaussian Processes [12, 18, 28], Artificial Neural Networks (ANNs) [12, 13], Recursive Neural Networks (RNN) [20], Deep Learning [29], as well as Long Short-Term Memory (LSTM) networks [30]. For the task of the bridging of the micro-and macro-scales, the Equation-free (EF) multiscale framework, introduced back in the early 2000s years, [1, 31, 32] bypasses the need to extract explicit, closed form macroscopic/surrogate models of any type (e.g.