OpInf-LLM: Using LLMs to Solve Parametric PDEs via Operator Inference
A new framework called OpInf-LLM leverages large language models (LLMs) for parametric partial differential equation (PDE) solving through operator inference. The approach uses small amounts of solution data to accurately predict diverse PDE instances, including unseen parameters and configurations, and integrates seamlessly with LLMs for natural language tasks. This addresses the persistent trade-off between execution success rate and numerical accuracy in prior LLM-based code generation and transformer-based foundation models for PDE learning. The work is detailed in arXiv:2602.01493v2.
Key facts
- OpInf-LLM is an LLM parametric PDE solving framework via operator inference.
- It uses small amounts of solution data for accurate prediction.
- It handles unseen parameters and configurations.
- It integrates with LLMs for natural language tasks.
- Prior work faced a trade-off between execution success rate and numerical accuracy.
- The framework aims to solve PDEs across heterogeneous settings.
- LLMs have shown capabilities in code generation, symbolic reasoning, and tool use.
- The paper is available on arXiv with ID 2602.01493v2.
Entities
Institutions
- arXiv