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[2602.17607] AutoNumerics: An Autonomous, PDE-Agnostic Multi-Agent Pipeline for Scientific Computing
Summary
AutoNumerics is a multi-agent framework that autonomously designs and verifies numerical solvers for PDEs from natural language, outperforming existing neural approaches.
Why It Matters
This research addresses the challenges of designing numerical solvers for partial differential equations (PDEs), which are crucial in scientific computing. By leveraging an autonomous framework, it enhances accessibility and efficiency in solving complex mathematical problems, potentially transforming computational practices in various fields.
Key Takeaways
- AutoNumerics autonomously generates numerical solvers from natural language descriptions.
- The framework employs a coarse-to-fine execution strategy for improved efficiency.
- It includes a self-verification mechanism to ensure solver accuracy.
- Experiments show competitive accuracy compared to existing methods.
- The approach enhances accessibility for users with limited mathematical expertise.
Computer Science > Artificial Intelligence arXiv:2602.17607 (cs) [Submitted on 19 Feb 2026] Title:AutoNumerics: An Autonomous, PDE-Agnostic Multi-Agent Pipeline for Scientific Computing Authors:Jianda Du, Youran Sun, Haizhao Yang View a PDF of the paper titled AutoNumerics: An Autonomous, PDE-Agnostic Multi-Agent Pipeline for Scientific Computing, by Jianda Du and 2 other authors View PDF HTML (experimental) Abstract: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. S...
