arXiv：cs.LG· Qian Hu, Bin Fan, Yao Xiao, Zhicheng Lin, Meixin Xiong·· 4 小时前AI 评分27
TGSR-PINN：面向物理信息神经网络逆问题的目标引导选择性重加权迁移学习方法
Target-Guided Selective Reweighting for Physics-Informed Neural Network Inverse Problems: A Transfer Learning Approach
AI 导读
研究者提出 TGSR-PINN，一种目标证据驱动的表示修正方法，用于物理信息神经网络（PINN）逆问题的迁移学习。该方法迁移源网络权重与偏置但独立初始化目标物理参数，经目标短适应后用一阶泰勒敏感度与预激活方差对神经元打分，再借助高斯混合模型与排名回退生成弱适应信号，并对输入权重行和偏置施加有界选择性软衰减。
正文
Abstract: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.
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2607.05271 [cs.LG] |
| (or arXiv:2607.05271v3 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2607.05271 arXiv-issued DOI via DataCite |
Submission history
From: Bin Fan [view email]
[v1]
Mon, 6 Jul 2026 16:20:19 UTC (11,617 KB)
[v2]
Thu, 3 Sep 2026 15:49:17 UTC (3,713 KB)
[v3]
Wed, 7 Oct 2026 07:57:26 UTC (3,713 KB)
来源：arXiv：cs.LG · arxiv.org