CodePDE: An Inference Framework for LLM-driven PDE Solver Generation
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arXiv
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| Main Authors: | , , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915811535355904 |
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| author | Li, Shanda Marwah, Tanya Shen, Junhong Sun, Weiwei Risteski, Andrej Yang, Yiming Talwalkar, Ameet |
| author_facet | Li, Shanda Marwah, Tanya Shen, Junhong Sun, Weiwei Risteski, Andrej Yang, Yiming Talwalkar, Ameet |
| contents | 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 solving agents, and failure modes for LLM on hard tasks. These insights offer guidance for building more capable and reliable LLM-based scientific engines. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_08783 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | CodePDE: An Inference Framework for LLM-driven PDE Solver Generation Li, Shanda Marwah, Tanya Shen, Junhong Sun, Weiwei Risteski, Andrej Yang, Yiming Talwalkar, Ameet Machine Learning Artificial Intelligence Computation and Language Numerical Analysis 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 solving agents, and failure modes for LLM on hard tasks. These insights offer guidance for building more capable and reliable LLM-based scientific engines. |
| title | CodePDE: An Inference Framework for LLM-driven PDE Solver Generation |
| topic | Machine Learning Artificial Intelligence Computation and Language Numerical Analysis |
| url | https://arxiv.org/abs/2505.08783 |