Nonlinear dynamic models are the cornerstones of the virtual environments that underlie design, optimization, control, and policy decisions. Ideally, these models should be formed from first principles, to embody the knowledge of the process. However, first principles models often lack the nonlinear constructs needed to accurately represent the process observations and are abandoned in the absence of structural adaptation capacity. Alternatives are empirical models in the form of nonlinear auto-regressive moving average (NARMAX) models or recursive neural networks, but these model forms lack the conceptual underpinnings to be generalized. Methods are presented that derive and/or refine concise and mechanistically meaningful dynamic models from observations. At one extreme, models of poorly understood processes (lacking first principles models) are developed from the ground up through a broad search of the variable/parameter space. At the other extreme, the first principles models of better understood processes are used as the starting models but are refined by gradient-based adaptation to improve their representation capacity despite their parametric inaccuracies. Applications of these methods are discussed in macroeconomic modeling and controls.