Robots monitoring complex, spatiotemporal phenomena require rich, meaningful representations of the environment. This thesis presents methods for representing the environment as a dynamical system with machine learning techniques. Specifically, we formulate machine learning methods that lend to data-driven modeling of the phenomena. The data-driven modeling explicitly leverages theoretical foundations of dynamical systems theory. Dynamical systems theory offers mathematical and physically interpretable intuitions about the environmental representation. The contributions presented include distributed algorithms, online adaptation, uncertainty quantification, and feature extraction to allow for the actualization of these techniques on-board robots. The environmental representations guide robot behavior in developing strategies such as optimal sensing and energy-efficient navigation. The methods and procedures provided in this thesis were verified across complex, spatiotemporal environments and on experimental robots.