10 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…
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…
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…
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…
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…