The core methodology of ESSG includes the following themes:

**Information Topologies for Estimation, Control and Inference:**In order to overcome the curse of nonlinearity and dimensionality, we study scale-space organization of graphical models where inference is conducted using tractable (quadratic) information summary measures. Our investigations center around: 1) system identification: finding the optimal topology for the graphical model, 2) inference using tractable alternatives to Shannon entropy, and 3) developing stochastic optimization procedures that can recover deep minima in an information potential framework. This technique is applied to data assimilation, uncertainty quantification, model reduction, pattern recognition, super-resolution and adaptive observation problems.**Statistical Theory of Inference for Coherent Fluids**Localized structures-- abundant in fluids-- are easily viewed as patterns. They are used to describe phenomenology, and even used in modeling. However, coherence has largely been ignored in fluid inference problems. Our research examines ways to utilize pattern information inherent in coherent fluids for solving inference problems such as spatial estimation, uncertainty quantification, super-resolution (or downscaling), model reduction, Nowcasting, among many others.**Pattern Recognition from Sparse Relevance Feedback**We study ways to represent features of surfaces by appearance and geometry to determine similarity. We are particularly motivated by using parsimony principles to determine similarity, and in the role that sparse human feedback (in the form of yes/no responses) can be used to improve pattern recognition and image processing performance.**Learning Simple Models of Complex Systems**: We are interested in finding methods to develop succinct, robust models of physical phenomena using data-driven approaches to augment physics, and vice versa. Applications include simplified hurricane and storm surge models, diagnosing model error, and quantifying uncertainty rapidly.**Learning Policies with Uncertain Probabilities**: Hazard mitigation, uncertainty propagation, adaptive sampling, and cooperative control must each contend with learning from data, generated either by measurements or models. The true distributions under which the stochastic inference problems associated problems**Instruments with Beliefs and Context**: We think that just a little physics and expectation from physics (how can the environment be roughly expected to behave) allows for the development of instruments with new sensitivity for detection and measurement. The closed system uses measurements to constrain the physical model of the expected environment, and for its predictions to target the sensitivity, range, and scope of the instrument.**Dynamics & Data in Environmental Systems Science**Our group seeks to develop dynamic data-driven application systems (DDDAS) that improve observations and measurements by modeling the environment in which the "instruments" are measuring. Interests include autonomous observation of small-scale atmospheric phenomena, experimental laboratory fluid dynamics, and computational photography for fluids, where we are having much fun!