Mathematical Methods

Developing Tools of Dynamical Systems for Broad Application

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    Bifurcation Structure for Large Amplitude Water Waves

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    Compresssive Sensing Architecture with Point Measurements

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    Poincare Dynamics for a Dispersion Map in Nonlinear Schrodinger Equation

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    Multi-Scale Physics Modeling via Multi-Resolution Dynamic Mode Decomposition

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    Learned Libraries of Dynamic Modes in Flow Around a Cylinder

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    Data Reduction and Sparse Classification

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    Compressive Sensing for Classification and Reconstruction of Flow

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    Proper Orthogonal Decomposition Modes for Flow Around a Cylinder

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    Band Gap Structure in Nonlinear Schrodinger Equation with Periodic Potential

Mathematical Methods Development and Application

 

My background is in traditional applied mathematics methods from partial differential equations, dynamical systems, asymptotic and perturbation theory, and scientific computing. I originally did quite a bit of work on understanding the stability and bifurcation structure of localized solutions of nonlinear wave equations. Over the past 5 years, I have branched out into the data sciences and have developed a theoretical interest in applications of data methods to dynamical systems, including machine learning, compressive sensing, equation-free modeling and reduced-order modeling. Please click on the sublinks above to see specific areas of theoretical interest.
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