发表机构
School of Advanced Interdisciplinary Sciences, University of Chinese Academy of Sciences; Institute of Automation, Chinese Academy of Sciences（中国科学院大学先进交叉科学学院; 中国科学院自动化研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
EvoPINN是智能体式框架，将PINN开发转化为基于执行的算法发现，通过LLM智能体迭代优化，自主发明SLRC-PINN，可显著降低PDE求解的相对L₂误差，为科学计算提供新机制。
AI 中文摘要
物理信息神经网络（Physics-Informed Neural Networks, PINNs）已成为求解偏微分方程（Partial Differential Equations, PDEs）的强大范式，但其性能高度依赖于对神经表征、损失函数和优化动态的人工试错式工程设计。尽管大型语言模型（Large Language Models, LLMs）为自动化设计提供了有前景的途径，但无约束的代码生成往往会在严格的科学计算约束下产生数学上无效或数值不稳定的解决方案。为弥合这一差距，我们提出了EvoPINN，这是一个智能体式框架，将PINN开发从费力的人工设计重新表述为严格的、基于执行的算法发现问题。EvoPINN通过将神经表征与训练程序解耦，在模块化搜索空间中进行探索，利用LLM智能体迭代提出基于内存的程序修改方案。为确保科学有效性，所有候选方案都经过严格的结构验证和与预算匹配的PDE评估。在不同的PDE regime（振荡型、椭圆型、耗散型和非线性输运型）上进行的大量实验表明，EvoPINN发现的PDE专用学习算法与基线相比显著降低了相对L₂误差。关键的是，EvoPINN自主发明了SLRC-PINN，这是一种新的架构，其性能提升在严格的参数匹配对比下依然存在，确立了基于执行的智能体用于发现真正新的科学计算机制的可行性。
英文摘要
Physics-informed neural networks (PINNs) have emerged as a powerful paradigm for solving partial differential equations (PDEs), yet their performance heavily relies on the manual, trial-and-error engineering of neural representations, loss formulations, and optimization dynamics. While Large Language Models (LLMs) offer a promising avenue for automated design, unconstrained code generation often yields mathematically invalid or numerically unstable solutions under strict scientific computing constraints. To bridge this gap, we propose \textbf{EvoPINN}, an agentic framework that reformulates PINN development from labor-intensive manual design into a rigorous, execution-grounded algorithm discovery problem. EvoPINN navigates a modular search space by decoupling neural representations from training programs, utilizing an LLM agent to iteratively propose memory-conditioned programmatic modifications. To ensure scientific validity, all candidates undergo strict structural verification and budget-matched PDE evaluation. Extensive experiments across diverse PDE regimes (oscillatory, elliptic, dissipative, and nonlinear transport) demonstrate that EvoPINN discovers PDE-specialized learning algorithms that significantly reduce relative $L_{2}$ error compared to baselines. Crucially, EvoPINN autonomously invented SLRC-PINN, a novel architecture whose performance gains persist under rigorous parameter-matched comparisons, establishing the viability of execution-grounded agents for discovering genuinely new scientific computing mechanisms.
