arXiv：cs.AI· Han Wan, Rui Zhang, Hao Sun·· 5 小时前
大语言模型如何应用于偏微分方程工作流：一篇综述
Large language models for partial differential equation workflows
AI 导读
一篇综述系统梳理了 LLM 辅助 PDE 研究的三个阶段：发现、求解与优化，考察 LLM 如何结合物理知识、数值方法和计算反馈来构建模型、实现求解流程并指导设计与控制。文章还回顾了评估科学有效性、计算性能与工作流可靠性的现有基准和实践，并提出三个方向：面向特定 PDE 问题的数学与物理推理、通过领域专用与多模态后训练构建可迁移专业知识、以及将主动实验设计与科学验证结合。
正文
Abstract:Numerical methods and deep learning have advanced the modelling and simulation of systems governed by partial differential equations (PDEs), while formulating equations, configuring solvers, and translating simulations into design and control decisions continue to demand substantial domain expertise and computational resources. Large language models (LLMs) offer opportunities to automate and coordinate these tasks by combining scientific knowledge, mathematical reasoning, code generation, and tool use. Here we review LLM-assisted PDE research across three stages, including discovery, solving, and optimization. We examine how LLMs interact with physical knowledge, numerical methods, and computational feedback to formulate models, implement solution procedures, and guide design and control. We also review existing benchmarks and evaluation practices for assessing scientific validity, computational performance, and workflow reliability. Finally, we discuss three interconnected challenges and opportunities: developing mathematical and physical reasoning tailored to specific PDE problems; building transferable domain expertise through domain-specific and multimodal post-training; and integrating active experimental design with scientific validation for open-ended problems. These directions outline a path towards a more substantive role for LLMs in developing and testing scientific ideas and computational methods across PDE research.
| Subjects: | Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2608.03600 [cs.AI] |
| (or arXiv:2608.03600v3 [cs.AI] for this version) | |
| https://doi.org/10.48550/arXiv.2608.03600 arXiv-issued DOI via DataCite |
Submission history
From: Han Wan [view email]
[v1]
Tue, 4 Aug 2026 12:51:32 UTC (3,690 KB)
[v2]
Sun, 20 Sep 2026 07:53:35 UTC (3,727 KB)
[v3]
Sun, 11 Oct 2026 08:17:22 UTC (3,698 KB)
来源：arXiv：cs.AI · arxiv.org