Abstract :

Reliable high-resolution state estimates for forecasts and reanalyzes are pivotal in environmental applications, particularly in ocean and atmospheric sciences. These are typically achieved by integrating observational data into dynamical models through processes such as data assimilation (DA), when enhancing the reliability of forecasts and reanalyzes, or downscaling when bridging the gap between coarse-scale observations and fine-scale information. Current DA and downscaling techniques rely on limiting assumptions and tend to be computationally demanding, especially in the presence of observational and model uncertainties. Artificial intelligence (AI) emerges as a powerful avenue for developing efficient data-driven tools that enhance reliability and alleviate computational demands of conventional DA and downscaling algorithms.

This dissertation aims to develop and test AI tools that address challenges falling under two themes, downscaling and DA with application to chaotic dynamical systems, and within an uncertain framework. The state of the art dynamical downscaling algorithm, Continuous data assimilation (CDA), and its discrete-in-time counterpart (DDA) are first explored in the setting involving observational errors. Since CDA relies on an abstract lifting function called the determining form map, a physics-informed deep neural network (PI-DNN) named CDAnet is proposed to approximate this intractable mapping. CDAnet is then evaluated under observational and model uncertainties in application to the Rayleigh--B\'enard convection problem, validating and further extending upon the knowledge from theory.

On the DA front, a PI-DNN is introduced for backward time predictions, central to the 4D-Var variational DA algorithm, which employs a linearized adjoint model. The PI-DNN offers reliable backward time predictions across various input temporal resolutions and time delays, offering a nonlinear counterpart to the tangent linear model. Finally, to address limitations in the ensemble Kalman filter (EnKF) DA algorithm, deep reinforcement learning (RL) is integrated into DA to actively update the nonlinear forecast correction scheme with incoming data. The RL framework outperforms the EnKF in application to the Lorenz '63 system across diverse scenarios, including different observational noise levels, noise models, observation frequencies, and partial observations

Bio :

Abed is currently a PhD candidate in the mechanical engineering program under the supervision of Profs. Omar Knio and Ibrahim Hoteit. Abed received his BEng in mechanical engineering from the American University of Beirut in 2018 and MSc in mechanical engineering from KAUST in 2020. His research at KAUST is interdisciplinary covering state estimation, artificial intelligence, marine pollution, risk assessment and uncertainty quantification.