12 papers
AutoPDE: Reliable Agentic PDE Solving via Explicitly Represented Solver Strategies
Huanshuo Dong, Keyao Zhang, Hong Wang +6
Numerical solvers for partial differential equations (PDEs) are core computational tools in science and engineering. Building reliable PDE solvers requires not only executable code…
AOT-POT: Adaptive Operator Transformation for Large-Scale PDE Pre-training
Qitan Lv, Hong Wang, Zhongkai Hao +5
Pre-training neural operators on diverse partial differential equation (PDE) datasets has emerged as a promising direction for building general-purpose surrogate models in scientif…
DSO: Dual-Scale Neural Operators for Stable Long-term Fluid Dynamics Forecasting
Huanshuo Dong, Hao Wu, Hong Wang +2
Long-term fluid dynamics forecasting is a critically important problem in science and engineering. While neural operators have emerged as a promising paradigm for modeling systems…
An Exterior-Embedding Neural Operator Framework for Preserving Conservation Laws
Huanshuo Dong, Hong Wang, Hao Wu +5
Neural operators have demonstrated considerable effectiveness in accelerating the solution of time-dependent partial differential equations (PDEs) by directly learning governing ph…
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…
SymMaP: Improving Computational Efficiency in Linear Solvers through Symbolic Preconditioning
Hong Wang, Jie Wang, Minghao Ma +2
Matrix preconditioning is a critical technique to accelerate the solution of linear systems, where performance heavily depends on the selection of preconditioning parameters. Tradi…
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…
Accelerating Data Generation for Neural Operators via Krylov Subspace Recycling
Hong Wang, Zhongkai Hao, Jie Wang +4
Learning neural operators for solving partial differential equations (PDEs) has attracted great attention due to its high inference efficiency. However, training such operators req…