Machine learning applications to dynamical and multi-agent systems

In this thesis, we focus on machine learning (ML) techniques as modelling tools for dynamical problems. We do not aim at testing ML in extreme conditions, but, rather, we try to apply it to interesting and controlled problems, focusing more on the physics and its modelling, rather than on the technique itself. First, we focus on effective models for multiscale chaotic systems. In the first work, we used an echo state neural network for reconstructing the slow part of a multiscale system. We show that such ML modelling has a physical interpretation as an asymptotic technique when the scale-separation is strong, but still works when such technique would fail. Moreover, we show how the hybrid (data+physics) framework both improves average performance and robustness. In the second work, we apply a ML technique to the macroscopic dynamics of a system of coupled maps. We show that it is possible to build an effective macroscopic dynamics and to uncover unknown macroscopic properties of the system, including memory effects, dimension and coarse graining structure. Second, we focus on biologically inspired multi-agent systems, where the self-interested nature of behaviours can be mimicked by optimization techniques. In the third work, we model the dynamics of two idealized microswimmers, a prey and predator, living in a low-Reynolds aquatic environment. We use reinforcement learning (RL) to let them discover appropriate behaviours, assuming they rely on hydrodynamic cues alone, thus tackling the problem of navigation with limited sensing, an important theme both in robotics and biology. We describe and interpret emerging strategies and highlight possible general patterns. The last work does not directly use ML, but optimal control, which is tightly connected to RL. Specifically, we deal with the optimal behaviour of an idealized swarm of active Brownian particles, which try to minimize collisions with minimum effort. We provide a mean-field characterization of their optimal behaviour; moreover, our results suggest that simple control functions may be used to describe near-optimal behaviours in such systems.