arXiv:2607.05271cs.LG2026-07被引 1

针对物理神经网络逆问题,提出目标引导的加权重调方法,提升参数恢复准确率。

Target-Guided Selective Reweighting for Physics-Informed Neural Network Inverse Problems: A Transfer Learning Approach

论文配图:Target-Guided Selective Reweighting for Physics-Informed Neural Network Inverse Problems: A Transfer Learning Approach
图 1 · 摘自论文原文
  • 基于目标证据动态调整低贡献神经元的权重,避免负迁移
  • 在高佩克莱特数与跨方程族任务中显著改善参数恢复精度
  • 适合需要精准物理参数估计的科学计算场景

物理信息神经网络(PINNs)在偏微分方程(PDE)逆问题中面临优化病态、损失竞争和参数补偿问题。迁移学习虽可复用源任务表征,但当源域与目标域的主导物理机制、控制参数或观测噪声不同时,直接微调可能导致负迁移:场误差低却恢复错误的物理参数。为此,本文提出目标引导的选择性重加权PINN(TGSR-PINN),一种目标证据驱动的表征修正方法。TGSR-PINN仅迁移源PINN的权重与偏置,而目标物理参数独立初始化;经短时目标适应后,利用一阶泰勒灵敏度与预激活方差,在固定评分批次上计算神经元目标得分,并通过带有秩回退的高斯混合模型(GMM)将低得分神经元的证据转化为连续弱适应信号。随后对低得分神经元的输入权重行与偏置施加选择性软衰减,而非硬剪枝或随机重置。实验表明,TGSR-PINN在高佩克莱特数2D对流-扩散任务及从Allen-Cahn到Burgers跨方程族迁移任务中,均在保持相近场精度的同时显著提升目标参数恢复性能;5%噪声的反应-扩散案例进一步验证了其在较弱源-目标差异下的有效性。消融实验证明,神经元目标评分、弱适应信号估计、层保护与选择性软衰减共同带来性能提升。

原文摘要 · Abstract (English)

Physics-informed neural networks (PINNs) encounter ill-posed optimization, loss competition, and parameter compensation in partial differential equation (PDE) inverse problems. Transfer learning can reuse representations from source tasks, but direct fine-tuning may introduce negative transfer when dominant physical mechanisms, governing parameters, or observation noise differ between source and target domains: the model achieves low field error yet recovers incorrect target physical parameters. To mitigate, we propose Target-Guided Selective Reweighting PINN (TGSR-PINN), a target-evidence-driven representation correction method for PINN inverse transfer learning. TGSR-PINN transfers only the weights and biases from the source PINN, while target physical parameters are independently initialized; after a short target-adaptation phase, the method computes neuron target scores using first-order Taylor sensitivity and pre-activation variance on fixed scoring batches, and converts evidence associated with low-scoring neurons into continuous weak-adaptation signals via a Gaussian mixture model (GMM) with rank fallback. TGSR-PINN then applies selective soft decay to input weight rows and biases of low-scoring neurons instead of hard pruning or random resetting. In experiments, TGSR-PINN improves target parameter recovery while maintaining comparable field accuracy in the high-Péclet 2D advection-diffusion task and in the Allen--Cahn to Burgers cross-PDE-family transfer task; a 5%-noise reaction--diffusion case provides supplementary evidence under milder source-target mismatch. Ablation studies suggest that neuron target scoring, weak-adaptation signal estimation, layer protection, and selective soft decay jointly contribute to the benefits.

物理信息网络逆问题迁移学习参数恢复

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