AutoNumerics: An Autonomous, PDE-Agnostic Multi-Agent Pipeline for Scientific Computing

• URL: http://arxiv.org/abs/2602.17607v1
• Date: Thu, 19 Feb 2026 18:31:52 GMT
• Title: AutoNumerics: An Autonomous, PDE-Agnostic Multi-Agent Pipeline for Scientific Computing
• Authors: Jianda Du, Youran Sun, Haizhao Yang,
• Abstract summary: We introduce textttAutoNumerics, a framework that autonomously designs, implements, debugs, and verifies numerical solvers for general PDEs directly from natural language descriptions.<n>Experiments on 24 canonical and real-world PDE problems demonstrate that textttAutoNumerics achieves competitive or superior accuracy.
• Score: 5.681456272022905
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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