5 papers
SAV Schemes with Decomposition-Induced Pullback Corrections for Gradient Flows
Shiheng Zhang, Jie Shen
The scalar auxiliary variable (SAV) method constructs linear, unconditionally energy-stable time discretizations of gradient flows. Eliminating the auxiliary variable in a first-or…
SAV-based entropy-dissipative schemes for a class of kinetic equations
Shiheng Zhang, Jie Shen, Jingwei Hu
We introduce novel entropy-dissipative numerical schemes for a class of kinetic equations, leveraging the recently introduced scalar auxiliary variable (SAV) approach. Both first a…
Structure preserving schemes for a class of Wasserstein gradient flows
Shiheng Zhang, Jie Shen
We introduce in this paper two time discretization schemes tailored for a range of Wasserstein gradient flows. These schemes are designed to preserve mass, positivity and to be uni…
An Element-wise RSAV Algorithm for Unconstrained Optimization Problems
Shiheng Zhang, Jiahao Zhang, Jie Shen +1
We present a novel optimization algorithm, element-wise relaxed scalar auxiliary variable (E-RSAV), that satisfies an unconditional energy dissipation law and exhibits improved ali…
Energy-Dissipative Evolutionary Deep Operator Neural Networks
Jiahao Zhang, Shiheng Zhang, Jie Shen +1
Energy-Dissipative Evolutionary Deep Operator Neural Network is an operator learning neural network. It is designed to seed numerical solutions for a class of partial differential…