发表机构
Shanghai Institute of Intelligent Education, East China Normal University, Shanghai; College of Artificial Intelligence, Nankai University（上海智能教育研究所，华东师范大学，上海; 人工智能学院，南开大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究针对物理信息神经网络（PINNs）设计敏感的问题，提出用进化算法引导大语言模型跨代生成可执行配置，经一维波动方程实验验证可行性，能降低均方误差，还揭示了低解误差与高PDE残差可共存等情况。
AI 中文摘要
物理信息神经网络（PINNs）对架构、激活、损失加权、配置、优化和约束执行等相互作用的选择异常敏感。大语言模型（LLMs）可以提出这些选择，但独立的建议不会从先前训练的PINNs中积累经验。我们提出了一种闭环进化算法，该算法引导LLMs跨代生成完整、可执行的PINN配置，利用测量的训练结果来确定后续的搜索决策。算法维护一个评估的种群和谱系，应用基于父代的变异和交叉，保留精英和多样化的解决方案，拒绝有效的重复项，并将与父代相关的成功和失败转化为提供给LLMs的下一代上下文。每个提议的配置都在精确的优化器步骤预算下直接执行。在一维多尺度波动方程上，两次独立的十代运行训练了60个PINNs，共进行600,000次优化器步骤。在两次运行中，最佳配置都出现在最后一代，相对于初始种群，最佳均方误差分别降低了2.97%和95.38%。较强的一次运行验证了残差连接并增加了单独分支的深度，在下一代中将它们组合起来，然后细化宽度和配置密度。它还表明低解误差可以与高偏微分方程残差共存。这些结果证明了进化算法引导的LLMs用于在受控偏微分方程上进行PINN设计的可行性，同时激发了更广泛的、具有物理意识的评估。
英文摘要
Physics-informed neural networks (PINNs) are unusually sensitive to interacting choices of architecture, activation, loss weighting, collocation, optimization, and constraint enforcement. Large language models (LLMs) can propose these choices, but independent recommendations do not accumulate experience from previously trained PINNs. We propose a closed-loop evolutionary algorithm that guides an LLM to generate complete, executable PINN configurations across generations, using measured training outcomes to determine subsequent search decisions. The algorithm maintains an evaluated population and lineage, applies parent-conditioned mutation and crossover, preserves elite and diverse solutions, rejects effective duplicates, and converts parent-relative successes and failures into the next-generation context supplied to the LLM. Every proposed configuration is executed directly under an exact optimizer-step budget. On a one-dimensional multiscale wave equation, two independent ten-generation runs trained 60 PINNs for 600,000 optimizer steps. In both runs, the best configuration appeared in the final generation, with best mean-squared error reduced by 2.97\% and 95.38\% relative to the initial population. The stronger run validated residual connections and increased depth on separate branches, combined them in a later generation, and then refined width and collocation density. It also revealed that low solution error can coexist with a high PDE residual. These results demonstrate the feasibility of evolutionary-algorithm-guided LLMs for PINN design on a controlled PDE while motivating broader, physics-aware evaluation.
