发表机构
School of Computing and Data Science, Fujian University of Technology（福建工程学院计算与数据科学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对物理信息神经网络逆问题迁移学习中的负迁移问题，提出TGSR-PINN方法，通过神经元目标评分与选择性软衰减，提升目标物理参数恢复精度。
AI 中文摘要
物理信息神经网络（PINNs）在偏微分方程（PDE）逆问题中会遇到不适定优化、损失竞争与参数补偿问题。迁移学习可复用源任务的表征，但当源域与目标域的主导物理机制、控制参数或观测噪声存在差异时，直接微调可能引发负迁移：模型可实现较低的场误差，却恢复出错误的目标物理参数。为缓解该问题，本文提出目标引导选择性重加权PINN（TGSR-PINN），一种用于PINN逆迁移学习的目标证据驱动表征校正方法。TGSR-PINN仅迁移源PINN的权重和偏置，目标物理参数则独立初始化；在短时间的目标适配阶段后，该方法在固定评分批次上利用一阶泰勒敏感度和预激活方差计算神经元目标评分，并通过带秩回退的高斯混合模型（GMM）将与低评分神经元关联的证据转换为连续的弱适配信号。随后TGSR-PINN对低评分神经元的输入权重行和偏置施加选择性软衰减，而非硬剪枝或随机重置。实验中，在高佩克莱数二维对流扩散任务以及Allen-Cahn到Burgers的跨PDE族迁移任务中，TGSR-PINN在保持相当场精度的同时提升了目标参数恢复效果；5%噪声的反应扩散场景在更温和的源-目标失配条件下提供了补充证据。消融实验表明，神经元目标评分、弱适配信号估计、层保护与选择性软衰减共同促成了该方法的性能增益。
英文摘要
Physics-informed neural networks (PINNs) often face ill-posed optimization, competing losses, and parameter compensation in partial differential equation (PDE) inverse problems. Transfer learning can reuse source-task representations, but direct fine-tuning may induce negative transfer when source and target physics differ, leading to low field error but inaccurate parameter recovery. To address this issue, we propose Target-Guided Selective Reweighting PINN (TGSR-PINN), a target-evidence-driven representation correction method for PINN inverse transfer learning. TGSR-PINN transfers source network weights and biases but initializes target physical parameters independently. After target short adaptation, it scores neurons using first-order Taylor sensitivity and pre-activation variance on fixed batches. These scores are converted into continuous weak-adaptation signals using a Gaussian mixture model with rank fallback. TGSR-PINN then applies bounded selective soft decay to the corresponding input weight rows and biases without pruning or resetting them. Experiments on a zero-source high-Péclet inflow-outflow problem with nonzero Dirichlet data and an outflow boundary layer, Allen-Cahn to Burgers cross-PDE transfer, and 5\%-noise reaction-diffusion inverse problems show that TGSR-PINN improves parameter recovery while maintaining low field error. Ablation studies indicate that neuron target scoring, weak-adaptation estimation, layer protection, and selective soft decay jointly contribute to the observed benefits.
