5 papers
Non-intrusive structural-preserving sequential data assimilation
Lizuo Liu, Tongtong Li, Anne Gelb
Data assimilation (DA) methods combine model predictions with observational data to improve state estimation in dynamical systems, inspiring their increasingly prominent role in ge…
Structurally informed data assimilation in two dimensions
Tongtong Li, Anne Gelb, Yoonsang Lee
Accurate data assimilation (DA) for systems with piecewise-smooth or discontinuous state variables remains a significant challenge, as conventional covariance-based ensemble Kalman…
The Bayesian SIAC filter
Jan Glaubitz, Tongtong Li, Jennifer Ryan +1
We propose the Bayesian smoothness-increasing accuracy-conserving (SIAC) filter -- a hierarchical Bayesian extension of the existing deterministic SIAC filter. The SIAC filter is a…
Entropy stable conservative flux form neural networks
Lizuo Liu, Tongtong Li, Anne Gelb +1
We propose an entropy-stable conservative flux form neural network (CFN) that integrates classical numerical conservation laws into a data-driven framework using the entropy-stable…
A Bayesian framework for spectral reprojection
Tongtong Li, Anne Gelb
Fourier partial sum approximations yield exponential accuracy for smooth and periodic functions, but produce the infamous Gibbs phenomenon for non-periodic ones. Spectral reproject…