AutoNumerics能自动设计基于自然语言的微分方程求解器，兼具准确与可解释性。
AutoNumerics: An Autonomous, PDE-Agnostic Multi-Agent Pipeline for Scientific Computing
- 多智能体协作，从自然语言直接生成数值求解器
- 在24个经典与真实问题上达到或超越现有方法精度
- 能根据方程结构自动选择合适数值方案，适合科研与工程应用
偏微分方程（PDEs）是科学与工程建模的核心，但设计高精度数值求解器通常需深厚数学功底和手动调参。近年基于神经网络的方法虽提升灵活性，却常伴随高计算成本与低可解释性。本文提出 exttt{AutoNumerics}，一个自主、无需领域知识的多智能体框架，可直接从自然语言描述中自动设计、实现、调试并验证通用PDE的数值求解器。不同于黑箱神经求解器，该框架生成基于经典数值分析的透明解法。引入粗粒度到细粒度执行策略及基于残差的自验证机制。在24个典型与实际应用的PDE问题上， exttt{AutoNumerics} 的精度与现有神经与LLM基线相当或更优，并能正确依据PDE结构特性选择数值格式，展现出作为自动化求解新范式的技术可行性。
原文摘要 · Abstract (English)
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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