发表机构
University of California, Los Angeles（加利福尼亚大学洛杉矶分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出AutoPDEBench基准，通过自主AI研究代理自动设计神经PDE求解器，在25个数据集上验证迭代自动化研究系统显著优于通用模型，证明AI代理可加速科学发现。
AI 中文摘要
偏微分方程（PDE）对于建模复杂物理系统至关重要，而神经求解器最近已成为数值求解这些方程的强大数据驱动工具。然而，现有的神经求解器在面对领域特定挑战（如参数变化和高速流动）时表现不佳，需要专门的架构。手动设计这些专门的求解器架构是一个高度迭代、耗时且需要深厚专业知识的过程，这成为科学发现中的重大瓶颈。我们提出利用自主人工智能研究代理来自动化专门求解器的合成。为此，我们引入了AutoPDEBench，一个专为LLM驱动的PDE求解器设计自动化研究而设立的基准。该基准包含25个具有挑战性的数据集，涵盖新颖且活跃研究的物理场景。我们评估了一系列通用模型（基于Transformer、ROM和图的方法）以及一个多代理实例化的迭代自动化研究流程，该流程作为代理基线。实证结果表明，迭代自动化研究系统显著优于通用神经求解器基线。我们的发现证明了使用AI代理自动设计复杂物理系统神经求解器的可行性。AutoPDEBench提供了一个基础测试平台，以加速物理和工程领域中代理驱动的科学发现。
英文摘要
Partial differential equations (PDEs) are essential for modeling complex physical systems, and neural solvers have recently emerged as powerful data-driven tools for numerically solving them. However, existing neural solvers struggle with domain-specific challenges, such as varying parameters and high-speed flows, necessitating specialized architectures. Manually designing these specialized solver architectures is a highly iterative, time-consuming process requiring deep expertise, creating a significant bottleneck in scientific discovery. We propose leveraging autonomous AI research agents to automate the synthesis of specialized solvers. To support this, we introduce AutoPDEBench, a benchmark dedicated to LLM-driven automated research for PDE solver design. The benchmark includes 25 challenging datasets featuring both novel and actively studied physical scenarios. We evaluate a suite of general-purpose models (transformer, ROM, and graph-based) alongside a multi-agent instantiation of the iterative automated research pipeline, which serves as an agentic baseline. Empirical results show that the iterative automated research system significantly outperforms the general-purpose neural solver baselines. Our findings demonstrate the viability of using AI agents to automatically design neural solvers for complex physical systems. AutoPDEBench provides a foundational testbed to accelerate agent-driven scientific discovery in physics and engineering.
