[CCoE Notice] Sequential Data Assimilation for Nonlinear Dynamical Systems - Wednesday Nov. 6th

[Knudsen, Rachel W]

Sequential Data Assimilation for Nonlinear Dynamical Systems

Dr. Mohammad Khalil, Sandia National Laboratories

Wednesday, November 6th, 10 am
Room 118, Melcher Hall, University of Houston

Abstract: The process of blending observational/field data with computational models of dynamical systems is known as data assimilation (DA). Data assimilation aims to find the optimal estimate of the state of dynamical systems using (a) the computational model describing the physical processes and (b) the noisy and sparse spatiotemporal data. DA methods are divided into two classes: variational and sequential methods. Variational DA provides a is based on optimal control theory and aims to minimize the data misfit as a function of unknown system parameters (for example the initial or boundary conditions) to provide the "best" state trajectory. On the other hand, sequential DA is based on a probabilistic framework which can handle arbitrary probability measures on the available data and unknown state. Sequential DA techniques assimilate data sequentially in time with the aim of improving forecast accuracy/precision. The Kalman filter has become a popular tool for sequential state estimation problems in linear systems. A number of extensions to the linear Kalman filter (e.g. extended Kalman filter, unscented Kalman filter and ensemble Kalman filter) have become popular tools for sequential data assimilation problems involving nonlinear systems. In the framework of Bayesian inference, the most general nonlinear filtering algorithm is the so-called particle filter which can handle general form of nonlinearities in model/measurement operators as well as non-Gaussian characteristics in the model/measurement errors. This talk will introduce sequential DA for nonlinear dynamical systems and the popular aforementioned techniques in comparison to the optimal solution obtained using the Fokker–Planck equation and Bayes' theorem.

In moving away from pure state estimation, nonlinear DA techniques have been recently utilized in solving the problem of static (time-invariant) parameter estimation in combination with Markov Chain Monte Carlo sampling strategies. These techniques have also been used in tackling Bayesian model selection with the aim of examining the suitability of many plausible models using the so-called model evidence. This presentation will provide an overview of such extensions of DA in Bayesian modeling workflows.


Bio: Mohammad Khalil is a Senior Member of the Technical Staff at Sandia National Laboratories, California in the Quantitative Modeling and Analysis department. He also holds an adjunct research professor position in the department of Civil & Environmental Engineering at Carleton University, Canada. He holds a B.Sc. in Microbiology and Immunology and a B.Eng. in Computer and Electrical Engineering from McGill University, Canada, and M.Sc. and Ph.D. degrees in Civil and Environmental Engineering from Carleton University, Canada. He has 15 years of experience developing Bayesian inference algorithms for statistical model calibration, parameter estimation, data assimilation, error modeling, and model selection, with applications in fluid-structure interaction, combustion modeling, radiation detection, nonlinear structural dynamics, wildfire forecasting, time-series analysis, and near-shore wave forecasting for energy harvesting.
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