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…
Evolve as a Team: Collaborative Self-Evolution for LLM-based Multi-Agent Systems
Zhezheng Hao, Tianfu Wang, Huanshuo Dong +7
LLM-based multi-agent systems (MAS) have emerged as an effective paradigm for complex and long-horizon tasks. However, in real-world tasks, MAS often exhibit various failures durin…
PDEAgent-Bench: A Multi-Metric, Multi-Library Benchmark for PDE Solver Generation
Zhen Hang, Yushan Yashengjiang, Junhui Li +21
PDE-to-solver code generation aims to automatically synthesize executable numerical solvers from partial differential equation (PDE) specifications. This task requires not only und…
N4MC: Neural 4D Mesh Compression
Guodong Chen, Huanshuo Dong, Mallesham Dasari
We present N4MC, the first 4D neural compression framework to efficiently compress time-varying mesh sequences by exploiting their temporal redundancy. Unlike prior neural mesh com…
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…
Accelerating IC Thermal Simulation Data Generation via Block Krylov and Operator Action
Hong Wang, Wenkai Yang, Jie Wang +6
Recent advances in data-driven approaches, such as neural operators (NOs), have shown substantial efficacy in reducing the solution time for integrated circuit (IC) thermal simulat…
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…