5 papers
A Conjugate Gradient Formulation of the EnKF Algorithm
Sanghyun Lee, Zhengqi Liu, Jonathan Valyou +1
Ensemble Kalman Filter (EnKF) based data assimilation algorithms synthesize predictive numerical forecast models with accumulated data as time evolves and account for model uncerta…
Superconvergence in finite element method by smoothing
Yuwen Li, Han Shui, Ludmil Zikatanov
This paper develops a smoothing-based postprocessing method for superconvergence in finite element methods. The method applies a few smoothing iterations, such as damped Jacobi, Ga…
A Mollification Approach to Ramified Transport and Tree Shape Optimization
Alberto Bressan, Giacomo Vecchiato, Ludmil Zikatanov
The paper analyzes a mollification algorithm, for the numerical computation of optimal irrigation patterns. This provides a regularization of the standard irrigation cost functiona…
Nodal auxiliary a posteriori error estimates
Yuwen Li, Ludmil T. Zikatanov
We introduce and explain key relations between a posteriori error estimates and subspace correction methods viewed as preconditioners for problems in infinite dimensional Hilbert s…
Neural networks with trainable matrix activation functions
Zhengqi Liu, Shuhao Cao, Yuwen Li +1
The training process of neural networks usually optimize weights and bias parameters of linear transformations, while nonlinear activation functions are pre-specified and fixed. Th…