Workshop: National Training workshop on fundamentals of Data Assimilation (NTDA-2)
Date & Venue: 06-10 February 2023, Meghdoot-IITM, Pune
Speaker: Prof. Laxmivarahan, George Lynn Cross Research Professor Emeritus, School of Computer science, University of Oklahoma, USA
Title & Abstract of the Course:
"Role of Observability Gramain in state and Parameter Estimation in Dynamical Systems”
The classical 4-D VAR method despite its great success is largely silent of the number and distribution of observations needed for effective estimation of the state and parameters in dynamical systems. Thanks to the advances in technology, as we move steadily from data sparse to data rich regimes, the cost of assimilating larges data set onlarge scale models become prohibitively large. To alleviate this computational burden, the question of selecting a proper subset of "influential observations" becomes very important. By combining the properties of the forward sensitivities of the model solution to the control consisting of the initial and boundary conditions and parameters, and the Jacobian of the forward operator, the structure of the observability Gramian is identified. An algorithm for identifying a minimal set of observations to render this observability Gramian positive definite provides a solution to the selection of an effective subset of observation to be used in data assimilation.
Lecture 1: Confluence of Data Science and AI/ML
Lecture 2: Challenges in Bigdata Analysis/ "Mathematics of Data Sciences"