  The advent of big data has vast potential for discovery in natural phenomena
ranging from climate science to medicine, but overwhelming complexity stymies
insight. Existing theory is often not able to succinctly describe salient
phenomena, and progress has largely relied on ad hoc definitions of dynamical
regimes to guide and focus exploration. We present a formal definition in which
the identification of dynamical regimes is formulated as an optimization
problem, and we propose an intelligible objective function. Furthermore, we
propose an unsupervised learning framework which eliminates the need for a
priori knowledge and ad hoc definitions; instead, the user need only choose
appropriate clustering and dimensionality reduction algorithms, and this choice
can be guided using our proposed objective function. We illustrate its
applicability with example problems drawn from ocean dynamics, tumor
angiogenesis, and turbulent boundary layers. Our method is a step towards
unbiased data exploration that allows serendipitous discovery within dynamical
systems, with the potential to propel the physical sciences forward.
