PINNForge：通过大型语言模型进行基于执行反馈的物理信息神经网络进化设计以求解偏微分方程

中文摘要 AI 辅助

物理信息神经网络（PINNs）需要在网络表示、采样、损失构建和优化方面进行协调选择，而有效的配置往往因偏微分方程（PDEs）的不同而有很大差异。现有的自动PINN设计方法可以搜索候选配置，但实际训练过程中揭示的信息仍主要用于评估，而非改进后续设计，导致反复试错和训练预算利用效率低下。我们提出了PINNsForge，一个基于LLM驱动的进化框架，用于基于执行反馈的自动PINN设计。PINNsForge从PDE相关的先验知识中生成多样化的候选配置，通过实际训练对其进行评估，并将高性能设计连同累积的执行证据反馈给LLM。在观察到的优化行为指导下，LLM随后细化、重组并探索耦合的PINN设计组件，形成生成、执行、反馈和进化的持续循环。与一次性搜索或仅评估反馈不同，PINNsForge逐步将训练经验转化为针对目标PDE的改进设计决策。在25个PDE基准测试中，与RoPINN、PINNsFormer和PINNsAgent相比，PINNsForge在24个任务上实现了最低的平均MSE。消融研究进一步证实了PDE知识库、执行反馈和进化搜索的重要性：移除这些组件分别使平均MSE增加到完整PINNsForge的3.74倍、12.10倍和10.10倍。

英文摘要

Physics-informed neural networks (PINNs) require coordinated choices across representation, architecture, sampling, constraints, loss construction, and optimization, yet effective configurations can vary substantially across partial differential equations (PDEs). Existing automated design methods search over these choices, but training outcomes are still used primarily to rank candidates rather than to inform subsequent designs. We develop PINNForge, an execution-grounded large language model (LLM)-driven evolutionary framework that treats observed PINN training behavior as a cross-generation design signal. PINNForge initializes diverse configurations from PDE-related prior knowledge, executes them, retains globally strong configurations, and feeds their execution evidence and accumulated run-level experience back to the LLM. The LLM then revises and recombines coupled design components or explores new combinations within a generate--execute--evaluate--evolve loop. Across 25 PDE benchmarks, PINNForge achieves the lowest mean MSE on 24 tasks among RoPINN, PINNsFormer, PINNsAgent, and PINNForge. Removing knowledge guidance, execution feedback, or evolutionary search increases the median task-wise MSE ratio to 3.74$\times$, 12.10$\times$, and 10.10$\times$, respectively, relative to full PINNForge.

发表机构

• Nankai University（南开大学）
• East China Normal University（华东师范大学）
• Hanyang University（汉阳大学）

机构由 AI 辅助整理，请以论文原文为准。