AI 中文总结
PINNMorph提出基于大语言模型引导策略演化的在线自适应框架，通过状态条件干预动态调整PINN训练，在13个PDE基准上超越现有方法，降低求解误差。
AI 中文摘要
物理信息神经网络（PINNs）提供了一种基于学习的框架用于求解偏微分方程（PDEs），但其训练行为在整个优化过程中可能发生显著变化。残差分布、梯度交互、区域学习难度以及模型容量需求可能随时间演变，而网络架构和主要训练机制通常在训练前就已确定。我们提出了PINNMorph，一种基于大语言模型（LLM）引导的策略演化的在线PINN自适应框架。PINNMorph维护一个状态条件自适应策略种群，这些策略将执行诊断映射为对拓扑修改、加性表示增强、目标平衡、梯度处理、自适应采样和优化器阶段控制的可控干预。在每个干预机会中，候选程序从当前策略种群中实例化，根据观察到的训练状态进行选择，并直接应用于正在训练的PINN。所得模型继承其现有参数和训练状态，并沿同一轨迹继续优化。执行结果随后用于评估干预并演化策略种群。与预训练架构搜索或固定自适应规则不同，PINNMorph利用实际训练的反馈，联合调整当前PINN及其干预策略。在13个PDE基准上的实验表明，PINNMorph在所有评估问题上均实现了比SA-PINN、ConFIG、RoPINN、HARMONIC和PINNsAgent更低的求解误差。消融研究进一步考察了在线自适应、状态条件干预选择和执行反馈驱动的策略演化的影响。
英文摘要
Physics-informed neural networks (PINNs) provide a learning-based framework for solving partial differential equations (PDEs), yet their training behavior can change substantially throughout optimization. Residual distributions, gradient interactions, regional learning difficulty, and model-capacity requirements may evolve over time, while the network architecture and major training mechanisms are typically determined before training. We propose PINNMorph, an online PINN adaptation framework based on large language model (LLM)-guided policy evolution. PINNMorph maintains a population of state-conditioned adaptation policies that map execution diagnostics to controlled interventions over topology modification, additive representation augmentation, objective balancing, gradient handling, adaptive sampling, and optimizer-phase control. At each intervention opportunity, candidate programs are instantiated from the current policy population, selected according to the observed training state, and applied directly to the PINN under training. The resulting model inherits its existing parameters and training state and continues optimization along the same trajectory. Execution outcomes are subsequently used to evaluate interventions and evolve the policy population. Unlike pre-training architecture search or fixed adaptation rules, PINNMorph jointly adapts the current PINN and the policies governing its interventions using feedback from actual training. Experiments on 13 PDE benchmarks show that PINNMorph achieves lower solution errors than SA-PINN, ConFIG, RoPINN, HARMONIC, and PINNsAgent across all evaluated problems. Ablation studies further examine the effects of online adaptation, state-conditioned intervention selection, and execution-feedback-driven policy evolution.
