Flocking in unbounded space: direct and inverse approaches to the weak cohesion problem

Active matter systems, composed of self-driven interacting units, provide a paradigmatic example of collective behavior far from equilibrium. Among these, flocking represents a striking form of large-scale organization, characterized by coherent motion and long-range correlations. While most theoretical and numerical studies have focused on bulk properties under periodic boundary conditions, much less attention has been devoted to finite, cohesive flocks evolving in unbounded space, as observed in natural systems. In this thesis, we investigate the physical characterization of cohesive, finite flocks that do not rely on a strongly ordered internal structure. We address this problem from two complementary perspectives. First, once weak cohesion is prescribed at the microscopic level, we ask how the size and shape of the resulting self-bound active object are selected, how its stability is maintained over long timescales, and which collective modes govern its large-scale deformations. Second, reversing the logic, we ask which local behavioral objectives are sufficient for the emergence of cohesive polar motion. To tackle these questions, we combine two complementary approaches. In a direct approach, we introduce a minimal Vicsek-like model in which alignment is supplemented by a weak social attraction and analyze the resulting finite flocks using both theoretical and numerical methods. We show that their global properties can be captured through a mode decomposition and demonstrate that these systems can exhibit underdamped collective shape oscillations despite purely overdamped microscopic dynamics. In an inverse approach, we employ a multi-agent reinforcement learning framework in which agents learn to balance attractive and aligning behavior from local information and biologically motivated objectives. We show that cohesive polar flocking can emerge from the combined requirement of staying together while avoiding potential collisions. Relaxing the latter constraint leads instead to cohesive but non-polar swarming states. Together, these results provide a unified perspective linking microscopic interactions and behavioral rules to the emergent static and dynamical properties of cohesive flocks in unbounded domains and contribute to the broader understanding of finite active systems in non-equilibrium statistical physics.