PhD Dissertation:
The majority of my research can be summarized as time-series predictions of chaotic systems after incorporating measurements. From here, my research can be split pretty neatly into two categories: model-free and model-based methods. The model-free approach belongs under the broad umbrella of machine learning and is known as Reservoir Computing, which was relatively new and unexplored at the time. The model-based approach belongs under the broad umbrella of Data Assimilation. It relies on a new paradigm of Data Assimilation where the constraint of having time-ordered states is loosened to just time-locality. We also use a Monte Carlo based optimizer in this approach, which was yet to be explored. Both these methods are tackled from the perspective of Data Assimilation and the understanding of nonlinear dynamics.

Post-PhD:
More recently, I am interested in understanding the theoretical and mathematical underpinnings of machine learning, through the lens and intuition of statistical physics and nonlinear dynamics. Recurrent Neural Networks, in particular the Reservoir Computing approach, and Data Assimilation appear to be related in a non-trivial way. The mechanism of Generalized Synchronization is clearly involved, which seems to be important in the development of Digital Twins. Not only is the theory of it all interesting, but new theory - as always - can lead to new ways of doing Data Assimilation. My hope is to apply such a worldview to develop low-fidelity Digital Twins of complex systems.