PhD thesis: Data-driven and learning-based approaches for the modeling, forecasting and reconstruction of geophysical dynamics: application to sea surface dynamics






Esporles, April 20, 2021. Said Ouala, department of Mathematical and Electrical Engineering, IMT Atlantique, Brest (France), has defended his doctoral thesis supervised by the doctors Ronan Fablet from IMT Atlantique, and Ananda Pascual from IMEDEA (CSIC-UIB). The event took place online on March 17.



This thesis focuses on the data-driven identification of dynamical representations of upper ocean dynamics for forecasting, simulation and data assimilation applications. We focus on practical considerations regarding the provided observations and tackle multiple issues, ranging from the parametrization of the models, their time integration, the space in which the models should be defined and their implementation in data assimilation schemes.


The core of our work resides in proposing a new data-driven embedding technique. This framework optimises an augmented space as a solution of an optimization problem, parametrised by a trainable Ordinary Differential Equation (ODE) that can be used for several applications such as forecasting and data assimilation. We discuss the effectiveness of the proposed framework within two different parametrizations of the trainable ODE. Namely, the Linear-quadratic and Linear ones and show that both formulations lead to interesting applications and most importantly, connect with interesting state-of-the-art theory that helps understanding and constraining the proposed architecture. Regarding data assimilation applications, we explore two distinct methodologies. The first technique can be seen as an alternative to the ensemble Kalman filtering and the second one relates to the proposed dynamical embedding technique and can be extended to match recent advances of state-of-the-art filtering techniques.