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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.17607 |
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| _version_ | 1866915807993266176 |
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| author | Du, Jianda Sun, Youran Yang, Haizhao |
| author_facet | Du, Jianda Sun, Youran Yang, Haizhao |
| contents | PDEs are central to scientific and engineering modeling, yet designing accurate numerical solvers typically requires substantial mathematical expertise and manual tuning. Recent neural network-based approaches improve flexibility but often demand high computational cost and suffer from limited interpretability. We introduce \texttt{AutoNumerics}, a multi-agent framework that autonomously designs, implements, debugs, and verifies numerical solvers for general PDEs directly from natural language descriptions. Unlike black-box neural solvers, our framework generates transparent solvers grounded in classical numerical analysis. We introduce a coarse-to-fine execution strategy and a residual-based self-verification mechanism. Experiments on 24 canonical and real-world PDE problems demonstrate that \texttt{AutoNumerics} achieves competitive or superior accuracy compared to existing neural and LLM-based baselines, and correctly selects numerical schemes based on PDE structural properties, suggesting its viability as an accessible paradigm for automated PDE solving. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_17607 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | AutoNumerics: An Autonomous, PDE-Agnostic Multi-Agent Pipeline for Scientific Computing Du, Jianda Sun, Youran Yang, Haizhao Artificial Intelligence Machine Learning Numerical Analysis PDEs are central to scientific and engineering modeling, yet designing accurate numerical solvers typically requires substantial mathematical expertise and manual tuning. Recent neural network-based approaches improve flexibility but often demand high computational cost and suffer from limited interpretability. We introduce \texttt{AutoNumerics}, a multi-agent framework that autonomously designs, implements, debugs, and verifies numerical solvers for general PDEs directly from natural language descriptions. Unlike black-box neural solvers, our framework generates transparent solvers grounded in classical numerical analysis. We introduce a coarse-to-fine execution strategy and a residual-based self-verification mechanism. Experiments on 24 canonical and real-world PDE problems demonstrate that \texttt{AutoNumerics} achieves competitive or superior accuracy compared to existing neural and LLM-based baselines, and correctly selects numerical schemes based on PDE structural properties, suggesting its viability as an accessible paradigm for automated PDE solving. |
| title | AutoNumerics: An Autonomous, PDE-Agnostic Multi-Agent Pipeline for Scientific Computing |
| topic | Artificial Intelligence Machine Learning Numerical Analysis |
| url | https://arxiv.org/abs/2602.17607 |