Curiosity-driven search for novel nonequilibrium behaviors

Exploring the full spectrum of novel behaviors that a system can produce can be an intensive task. Sampling techniques developed in response to this exploration challenge often require a predefined metric, such as distance in a space of known order parameters. However, order parameters are rarely known for nonequilibrium systems, especially in the absence of a diverse set of example behaviors, creating a chicken-and-egg problem. Here, we combine active and unsupervised learning for automated exploration of nonequilibrium systems with unknown order parameters. We iteratively use active learning based on current order parameters to expand the library of behaviors and relearn order parameters based on this expanded library. We demonstrate the utility of this approach in Kuramoto models of increasing complexity. In addition to reproducing known phases, we reveal previously unknown behavior and related order parameters, and we demonstrate how to align search with human intuition.