CAM Colloquium - Anne Gelb, Department of Mathematics, Dartmouth College

Title: Non-intrusive Structural-Preserving Sequential Data Assimilation Abstract: Data assimilation (DA) methods combine model predictions with observational data to improve state estimation in dynamical systems, inspiring their increasingly prominent role in geophysical and climate applications. Classical DA methods assume that the governing equations modeling the dynamics are known, which may not be true in real world applications. Machine learning (ML) provides a flexible alternative by learning surrogate models directly from data, but standard ML methods struggle in noisy and data-scarce environments, where meaningful extrapolation requires incorporating physical constraints. Recent advances in structure-preserving ML architectures, such as the development of the entropy-stable conservative flux form network (ESCFN), highlight the critical role of physical structure in improving learning stability and accuracy for unknown systems of conservation laws. Structural information has also been shown to improve DA performance. Gradient-based measures of spatial variability, in particular, can help refine ensemble updates in discontinuous systems. Motivated by both of these recent innovations, we propose a new non-intrusive, structure-preserving sequential data assimilation (NSSDA) framework that leverages structure at both the forecast and analysis stages. Our method operates in a highly constrained environment, using only a single noisy trajectory for both training and assimilation. Bio: Dr. Anne Gelb earned her Ph.D. and Sc.M. in Applied Mathematics from Brown University and a B.S. in Applied Mathematics from UCLA. She is currently the John G. Kemeny Parents Professor of Mathematics at Dartmouth College and previously held faculty positions at Arizona State University, following a postdoctoral fellowship at the California Institute of Technology. She is the principal investigator on a Department of Defense–funded MURI project focused on sea ice modeling and data assimilation, collaborating with researchers from Dartmouth, Arizona State, MIT, and CRREL. Her research focuses on numerical analysis and computational methods for partial differential equations, data assimilation, and signal and image processing, with applications including medical imaging, forecasting, fraud detection, and remote sensing. Her work emphasizes extracting critical information from indirectly acquired data and incorporating Bayesian methods to quantify uncertainty.