OpInf-LLM：基于算子推理用 LLM 求解参数化偏微分方程
OpInf-LLM: Parametric PDE Solving with LLMs via Operator Inference
AI 导读
研究者提出 OpInf-LLM，一个通过算子推理让大语言模型求解参数化偏微分方程（PDE）的框架。该框架仅需少量解数据，即可准确预测包括未见参数和配置在内的多样 PDE 实例，并与 LLM 的自然语言任务描述及物理推理无缝结合。其低计算开销与统一求解流程带来高执行成功率，缓解了执行成功率与数值精度之间的权衡。
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