Discovering the emergent nonlinear dynamics of acoustically levitated cube clusters

The complex behaviour of many natural and engineered systems emerges from the interaction of a small number of effective degrees of freedom. Discovering the physical basis of the interactions between these degrees of freedom directly from experimental observations has been a longstanding challenge, particularly with respect to predicting the long-time dynamics of dynamical systems with unknown equations of motion. Here, we present observations and fit a generative, data-driven model of a dynamical system with two degrees of freedom: acoustically levitated pairs of cube-shaped particles, which cluster by sharing a single edge. In the acoustic trap, the center-of-mass of the cube cluster oscillates vertically about the levitation plane, while also oscillating about their flexible hinge-like connection. Depending on their initial condition, the hinge dynamics evolve about three distinct nonlinear dynamical attractors persisting for hundreds of cycles. We numerically fit a minimal nonlinear dynamical model that captures both the long-time dynamics of the cluster as well as the convergence onto the dynamical steady state. This dynamical model uncovers the nonlinear, non-reciprocal coupling between the center-of-mass motion and the hinge degree of freedom that stabilizes the dynamical attractors, which we subsequently confirm by independent finite-element models. Our results demonstrate a novel data-driven method for the discovery of nonlinear models with long-timescale stable predictions.