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[2505.08783] CodePDE: An Inference Framework for LLM-driven PDE Solver Generation
Summary
The article presents CodePDE, an innovative framework leveraging large language models (LLMs) for generating solvers for partial differential equations (PDEs), addressing challenges in traditional and neural network-based methods.
Why It Matters
This research is significant as it explores the intersection of machine learning and numerical analysis, offering a novel approach to solving complex PDEs. By framing PDE solving as a code generation task, it opens new avenues for enhancing solver reliability and interpretability, which are crucial for scientific applications.
Key Takeaways
- CodePDE introduces a framework for generating PDE solvers using LLMs.
- It highlights the trade-offs between solver reliability and sophistication.
- The framework demonstrates strong performance across various PDE problems.
- Insights into failure modes and design principles for LLM-powered solvers are provided.
- The research guides the development of more capable LLM-based scientific engines.
Computer Science > Machine Learning arXiv:2505.08783 (cs) [Submitted on 13 May 2025 (v1), last revised 22 Feb 2026 (this version, v2)] Title:CodePDE: An Inference Framework for LLM-driven PDE Solver Generation Authors:Shanda Li, Tanya Marwah, Junhong Shen, Weiwei Sun, Andrej Risteski, Yiming Yang, Ameet Talwalkar View a PDF of the paper titled CodePDE: An Inference Framework for LLM-driven PDE Solver Generation, by Shanda Li and 6 other authors View PDF HTML (experimental) Abstract:Partial differential equations (PDEs) are fundamental to modeling physical systems, yet solving them remains a complex challenge. Traditional numerical solvers rely on expert knowledge to implement and are computationally expensive, while neural-network-based solvers require large training datasets and often lack interpretability. In this work, we frame PDE solving as a code generation task and introduce CodePDE, the first inference framework for generating PDE solvers using large language models (LLMs). With CodePDE, we present a thorough evaluation on critical capacities of LLM for PDE solving: reasoning, debugging, self-refinement, and test-time scaling. CodePDE shows that, with advanced inference-time algorithms and scaling strategies, LLMs can achieve strong performance across a range of representative PDE problems. We also identify novel insights into LLM-driven solver generation, such as trade-offs between solver reliability and sophistication, design principles for LLM-powered PDE solvin...
