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Meeting # 942 7359 5552

Zoom Meeting # 942 7359 5552

Abstract:

Data assimilation, also known as stochastic filtering, seeks to learn/estimate the evolving state of a physical system by combining a mathematical model with partial and noisy real observations. This process is formulated as a state-space model (SSM), where the objective is to refine state estimates and enhance future predictions in real-time applications (e.g. weather forecasting). However, filtering high-dimensional, nonlinear SSMs presents significant computational challenges. Particle filters offer an exact solution in theory, but their practical implementation suffers from the curse of dimensionality, requiring an exponentially large number of samples, $N = O(\kappa^d)$, with $\kappa > 1$. This makes them computationally prohibitive. An alternative is to use Markov Chain Monte Carlo (MCMC) sampling to generate realizations from the filtering distribution. However, since this distribution incorporates the entire state history up to the current time, MCMC’s computational complexity increases linearly with time, limiting its efficiency in real-time settings. In this talk, I will introduce two novelfiltering techniques designed to alleviate these computational burdens. The first replaces the standard smoothing distribution with a lagged approximation, effectively reducing dependencies between states. This modification, which integrates particle filtering with sequential Monte Carlo samplers, introduces a small bias that remains controlled in both dimension and time while ensuring a computational cost that grows polynomially with $d$. The second method utilizes sequential MCMC (SMCMC) to sample from a particular approximation of the filtering distribution, which is shown to be asymptotically exact. In many cases, the cost of this new algorithm scales linearly with $d$. Additionally, I will present a localized version of SMCMC that significantly reduces computational cost in cases where the available data is very sparse or highly localized.

Speaker's Bio

Dr. Hamza Ruzayqat is a Research Scientist at KAUST, interested in Applied Mathematics in general and Computational Probability/Statistics in particular. He is specialized in Monte Carlo algorithms, Data Assimilation, and Uncertainty Quantification & Inverse Problems. He earned his Ph.D. in Mathematics from the University of Tennessee-Knoxville, USA, in 2019 and a Bachelor degree in Physics from Birzeit University, Palestine. Dr. Ruzayqat joined KAUST in late 2019 as a postdoc before he became a research scientist in 2022. His research focuses on developing efficient stochastic or deterministic algorithms for real-world applications across science and engineering. Active areas of research include: Data assimilation techniques for nonlinear, high-dimensional state-space models, Bayesian inverse problems, fractional diffusions with fast solvers, multilevel and unbiased estimation.