Applied Analysis Seminar: Hristo G. Chipilski

About this event

Generative Techniques for Data Assimilation and Parameter Estimation: From Bayesian Theory to Geophysical Applications Generative techniques have emerged as powerful tools for approximating and sampling complex probability distributions, creating new opportunities for inference in geophysical systems. This talk will present a unifying Bayesian framework for data assimilation and parameter estimation: represent the prior distribution with a generative model, then introduce suitable likelihood approximations to make posterior inference tractable. The opening part of my talk will establish this common foundation and contrast it with approaches that learn to sample directly from posterior distributions. With this context in mind, I will first focus on deterministic, flow-based generative models defined by diffeomorphisms: smooth, invertible transformations connecting Gaussian reference distributions to complex, non-Gaussian distributions. I will introduce a conjugate transform theory for state estimation, in which a compatible likelihood structure enables Kalman updates in a latent Gaussian space. This framework will serve as a foundation for non-iterative Ensemble Conjugate Transform Inversion (ECTI) algorithms for Bayesian parameter estimation, followed by iterative extensions that generalize ensemble Kalman inversion (EKI). I will discuss existence, uniqueness, and convergence in the noise-free regime and illustrate these methods through idealized statistical examples and applications to cloud microphysics and subsurface flow. Second, I will turn to score-based diffusion models and introduce the Ensemble Score Filter (EnSF) for sequential data assimilation. Here, posterior sampling uses an empirically damped likelihood score evaluated at noisy diffusion states. This approximation recovers the exact likelihood score at the diffusion endpoints but introduces structural errors at intermediate times. I will explain how vanishing likelihood gradients in unobserved directions limit the original method under sparse observations, then present two extensions that propagate observational information across the state: a two-step update using linear regression, and a formulation incorporating localized covariances directly into the reverse diffusion dynamics. In addition to illustrating these generative algorithms in geophysical models, I will highlight some recent advances in using them for exascale computing on massively parallel architectures, enabling applications to realistic weather and climate problems. Bio Hristo joined Florida State University in 2023 as an Assistant Professor in the Department of Scientific Computing. Previously, he spent two years at the NSF National Center for Atmospheric Research (NSF NCAR) as a postdoctoral fellow in the Advanced Study Program. His current research focuses on developing algorithms at the intersection of data assimilation and AI/ML to improve the analysis and prediction of challenging Earth system processes. He earned his Ph.D. in Meteorology from the University of Oklahoma, where he demonstrated the value of assimilating ground-based remote sensing observations for convective-scale applications. He also studied hydraulic dynamics and used image processing techniques to develop an object-based algorithm for tracking atmospheric bores in numerical models. He is an active member of the American Meteorological Society (AMS), the American Geophysical Union (AGU), and the Society for Industrial and Applied Mathematics (SIAM), and serves as an Associate Editor for 3 different journals.