arXiv cs.AI· Zhuoyuan Wang, Hanjiang Hu, Xiyu Deng, Saviz Mowlavi, Yorie Nakahira·· 11 小时前AI 评分26
OpInf-LLM：基于算子推断的 LLM 参数化 PDE 求解框架
OpInf-LLM: Parametric PDE Solving with LLMs via Operator Inference
AI 导读
OpInf-LLM 是一个通过算子推断让 LLM 求解参数化 PDE 的框架，仅需少量解数据即可准确预测未见参数与边界条件下的 PDE 实例。该框架支持自然语言任务描述与基于物理的特征参数化推理，计算需求低且采用统一求解流程，在异构设置下实现高执行成功率。
正文 · 原文
Abstract:Solving diverse partial differential equations (PDEs) is fundamental in science and engineering. Large language models (LLMs) have demonstrated strong capabilities in code generation, symbolic reasoning, and tool use, but reliably solving PDEs across heterogeneous settings remains challenging. Prior work on LLM-based code generation and transformer-based foundation models for PDE learning has shown promising advances. However, a persistent trade-off between execution success rate and numerical accuracy arises, particularly when generalization to unseen parameters and boundary conditions is required. In this work, we propose OpInf-LLM, an LLM parametric PDE solving framework via operator inference. The proposed framework leverages small amounts of solution data to enable accurate prediction of diverse PDE instances, including unseen parameters and configurations, and provides seamless integration with LLMs for natural language task specification and physics-based reasoning of proper feature parameterization. Its low computational demands and unified solution pipeline further enable a high execution success rate across heterogeneous settings, opening new possibilities for generalizable reduced-order modeling in LLM-based PDE solving.
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2602.01493 [cs.LG] |
| (or arXiv:2602.01493v3 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2602.01493 arXiv-issued DOI via DataCite |
Submission history
From: Zhuoyuan Wang [view email]
[v1]
Mon, 2 Feb 2026 00:04:50 UTC (2,919 KB)
[v2]
Thu, 23 Apr 2026 01:22:58 UTC (2,923 KB)
[v3]
Wed, 4 Nov 2026 07:12:17 UTC (3,760 KB)
来源：arXiv cs.AI · arxiv.org