7 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 generalization of the existing deterministic SIAC filter. The SIAC filter…
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…
Very weak solutions of the Dirichlet problem for 2-Hessian equation
Tongtong Li, Guohuan Qiu
For any small, we construct infinitely many very weak solutions to the 2-Hessian equation with prescribed boundary value. The proof relies on the convex integration m…
A Structurally Informed Data Assimilation Approach for Nonlinear Partial Differential Equations
Tongtong Li, Anne Gelb, Yoonsang Lee
Ensemble transform Kalman filtering (ETKF) data assimilation is often used to combine available observations with numerical simulations to obtain statistically accurate and reliabl…