  Convection is a fundamental fluid transport phenomenon, where the large-scale
motion of a fluid is driven, for example, by a thermal gradient or an electric
potential. Modeling convection has given rise to the development of chaos
theory and the reduced-order modeling of multiphysics systems; however, these
models have been limited to relatively simple thermal convection phenomena. In
this work, we develop a reduced-order model for chaotic electroconvection at
high electric Rayleigh number. The chaos in this system is related to the
standard Lorenz model obtained from Rayleigh-Benard convection, although our
system is driven by a more complex three-way coupling between the fluid, the
charge density, and the electric field. Coherent structures are extracted from
temporally and spatially resolved charge density fields via proper orthogonal
decomposition (POD). A nonlinear model is then developed for the chaotic time
evolution of these coherent structures using the sparse identification of
nonlinear dynamics (SINDy) algorithm, constrained to preserve the symmetries
observed in the original system. The resulting model exhibits the dominant
chaotic dynamics of the original high-dimensional system, capturing the
essential nonlinear interactions with a simple reduced-order model.
