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math.NA2025
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…
math.NA2025
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…
math.NA2025
Neural Entropy-stable conservative flux form neural networks for learning hyperbolic conservation laws
Lizuo Liu, Lu Zhang, Anne Gelb
We propose a neural entropy-stable conservative flux form neural network (NESCFN) for learning hyperbolic conservation laws and their associated entropy functions directly from sol…