Equations of mind: Data science for inferring nonlinear dynamics of socio-cognitive systems

Discovering the governing equations for a measured system is the gold standard for modeling, predicting, and understanding complex dynamic systems. Very complex systems, such as human minds, pose stark challenges to this mode of explanation, especially in ecological tasks. Finding such “equations of mind” is sometimes difficult, if impossible. We introduce recent directions in data science to infer differential equations directly from data. To illustrate this approach, the simple but elegant example of sparse identification of nonlinear dynamics (SINDy; Brunton, Proctor, & Kutz, 2016) is used. We showcase this method on known systems: the logistic map, the Lorenz system, and a bistable attractor model of human choice behavior. We describe some of SINDy's limitations, and offer future directions for this data science approach to cognitive dynamics, including how such methods may be used to explore social dynamics.