6 papers · 1 filter
From Uniform to Adaptive: General Skip-Block Mechanisms for Efficient PDE Neural Operators
Lei Liu, Zhongyi Yu, Hong Wang +4
In recent years, Neural Operators(NO) have gradually emerged as a popular approach for solving Partial Differential Equations (PDEs). However, their application to large-scale engi…
Mixture-of-Experts Operator Transformer for Large-Scale PDE Pre-Training
Hong Wang, Haiyang Xin, Jie Wang +4
Pre-training has proven effective in addressing data scarcity and performance limitations in solving PDE problems with neural operators. However, challenges remain due to the heter…
STNet: Spectral Transformation Network for Solving Operator Eigenvalue Problem
Hong Wang, Jiang Yixuan, Jie Wang +3
Operator eigenvalue problems play a critical role in various scientific fields and engineering applications, yet numerical methods are hindered by the curse of dimensionality. Rece…
Accelerating Eigenvalue Dataset Generation via Chebyshev Subspace Filter
Hong Wang, Jie Wang, Jian Luo +4
Eigenvalue problems are among the most important topics in many scientific disciplines. With the recent surge and development of machine learning, neural eigenvalue methods have at…
Accelerating Data Generation for Nonlinear temporal PDEs via homologous perturbation in solution space
Lei Liu, Zhenxin Huang, Hong Wang +4
Data-driven deep learning methods like neural operators have advanced in solving nonlinear temporal partial differential equations (PDEs). However, these methods require large quan…
Accelerating PDE Data Generation via Differential Operator Action in Solution Space
Huanshuo Dong, Hong Wang, Haoyang Liu +2
Recent advancements in data-driven approaches, such as Neural Operator (NO), have demonstrated their effectiveness in reducing the solving time of Partial Differential Equations (P…