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My career began in experimental particle physics. Over time, I began working more with Applied Mathematicians on problem involving fluid flow, ultimately leading to studies of the ocean. My last five publications have focused on the Eulerian perspective of fluid flow, whereby the velocity vector field is analyzed in an absolute frame of reference as opposed to a particle centric approach (Lagrangian based). This work involves finding appropriate metrics in the Eulerian sector which may inform engineering decisions on micro-fluidic mixers, as well as developing Eulerian analytics which broaden the language with which we discuss flow.
Ultimately, working with ocean as a data set involves "Big Data" residing in a high-dimensional manifold which leads to the question: "Which measures of the flow characterize the observed behavior and lead to credible predictions?"
Throughout these studies, I have been able to map techniques I have either learned or developed to new data sets. Recently, I have been considering apply Dynamic Mode Decomposition (DMD) to the Arctic Sea Ice flow in the hopes of understanding the time dependence with possible predictions of the flow in the immediate future. Coupled to this, Physics Informed Neural Networks (PINN) are being applied in a rising number of applications, as Deep Learning is giving Neural Networks (NN) a new life. With respect to the Arctic, should a region of the Arctic Ocean become inaccessible to both naval traffic as well as data collection, can PINN help "fill in" the data gaps, allowing DMD to continue providing a window to the future? Both techniques are data-driven and assume nothing of the underlying physical system; instead, these techniques extract the relevant dynamics from the data itself - in other words - nature already has the correct physical system knowledge built into it, so data taken from observations of nature already contain correlated information regarding the system under study. DMD and PINN simply provide a framework to understand the results presented.