My primary research interest is in spontaneous self-organization in nonlinear dynamical systems. These emergent behaviors typically can not be deduced or derived from the governing equations of motion and thus pose an immense challenge to the traditional hypothesis-driven scientific paradigm. The current age of big data and data analytics offers an exciting opportunity to circumvent these difficulties with data-driven approaches for dynamical systems. I have primarily worked on an unsupervised methodology utilizing the nonparametric local causal state models. These models can capture patterns as generalized symmetries in spacetime, and coherent structures as localized deviations from these generalized symmetries. The local causal states can be viewed as a form of physics-based representation learning, and I have shown how they fit into the general autoencoder framework for learning representations. While analytics are of limited value for emergent self-organization, the physics encapsulated in the equations of motion can not be completely disregarded. I am interested in uncovering general principles of self-organization and how data-driven methods can help discover the physical and causal mechanisms that give rise to emergent pattern and structure, especially in the far-from-equilibrium regime. I work on both theory and applications, with a particular emphasis on Earth and Environmental Science.