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A brief overview of my interests
I obtained my PhD in Physics where I worked on problems in data assimilation. This generally make me fond of problems that involve applications of mathematical ideas and codes, bringing me closer to the realm of mathematical modelling, simulations and data. I am particulary fascinated by problems that arise in earth sciences from a dynamical systems perspective. Data assimilation is a crucial part that makes numerical weather prediction possible. I work on both classical data assimilation and deeplearning based data assimilation techniques, most of the times looking for an ideal way to use the best of both worlds.
On a daily basis, my daily work revolves around handling code of a physical systems model (Partial differential equations) and some deeplearning model ( neural network models, mostly in PyTorch) to solve a data assimilation problem.
A brief overview of my PhD research
My thesis research work concentrates around Data assimilation for chaotic dynamical system using EnKF (Evensen(2003)), a general sequential state estimation algorithm which computes the best estimate of the state with associated uncertainty. Data assimilation is a way to force the numerical model using observations from the real system in order to keep it near the true state of the system. It enables both short and long-term prediction by combining the model estimates and the observations in a statistially optimal way.
The underlying theme of my interests have been in studying filtering algorithms and their properties which can be used to diagnose and improve the same. In a joint work, I have worked on demonstrating numerical filter stability, a crucial property of a filter using Sinkhorn distance, a distances between probaility distribution. In another work, I am looking at instability properties of a dynamical system such as lyapunov vectors which are of potential utility in improving the existing techniques in prediction and estimation of a dynamical system in general. Now I talk about them in detail the following posts below.
Long-term vision of my research objective
I am interested in understanding ways to incorporate uncertainty and dynamical knowledge together to a general machine learning techniques for modelling and inference of large dynamical systems such as weather, climate and earth system model. The following is an overview of different research projects that I have worked over time.
