arXiv:2607.15560cs.NEcs.AI2026-07

用进化算法引导大模型自动设计物理信息神经网络,显著提升精度。

Evolutionary Algorithm-Guided LLMs for Physics-Informed Neural Network Design

  • 构建闭环进化框架,让大模型根据训练结果迭代生成完整PINN配置。
  • 两次独立实验中,最优配置在第10代出现,误差降低最高达95.38%。
  • 揭示深层结构与残差连接对精度的促进作用,适合从事科学计算的开发者。

物理信息神经网络(PINNs)对架构、激活函数、损失权重、采样点分布、优化策略和约束施加方式等选择极为敏感。大语言模型(LLMs)可提出这些配置,但无法积累过往训练经验。本文提出一种闭环进化算法,指导LLM在多代中生成完整可执行的PINN配置,并利用训练结果决定后续搜索方向。算法维护已评估种群与谱系,采用父代条件下的变异与交叉,保留精英与多样化解,剔除有效重复项,并将父代相对成败转化为下代提供给LLM的上下文。每个配置均在精确优化步数预算内直接执行。在一维多尺度波动方程上,两次独立的十代运行共训练60个PINN,总计60万次优化步骤。两轮实验中,最佳配置均出现在最终代,平均平方误差分别较初始种群降低2.97%和95.38%。强效果运行验证了残差连接与分支独立加深的有效性,后期合并后进一步优化宽度与采样密度;同时发现低解误差可与高PDE残差共存。结果表明该方法在控制型偏微分方程上可行,并推动更广泛、基于物理的评估机制发展。

原文摘要 · Abstract (English)

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.

PINNs进化算法大模型科学深度学习

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