Objective discovery of fluid dynamical regimes with unsupervised machine learning

Significant advances in the understanding and modeling of dynamical systems has been enabled by the identification of processes that locally and approximately dominate system behavior, or dynamical regimes. The conventional regime identification method involves tedious and ad hoc parsing of data to judiciously obtain scales to ascertain which governing equation terms are dominant in each fluid dynamical regime. Surprisingly, no objective and universally applicable criterion exists to robustly identify dynamical regimes in an unbiased manner, neither for conventional nor for machine learning-based methods of analysis. Here, we formally define dynamical regime identification as an optimization problem by using a verification criterion, and we show that an unsupervised learning framework can automatically and credibly identify regimes. This eliminates reliance upon conventional analyses, with vast potential to accelerate discovery. Our verification criterion also enables unbiased comparison of regimes identified by different methods. In addition to diagnostic applications, the verification criterion and learning framework are immediately useful for data-driven dynamical process modeling. Automation of this kind of approximate mechanistic analysis is necessary to search for new dynamical insights from increasingly large data streams.