{"ID":5936977,"CreatedAt":"2026-07-07T03:14:33.014478982Z","UpdatedAt":"2026-07-09T16:12:55.966383441Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.05271","arxiv_id":"2607.05271","title":"Target-Guided Selective Reweighting for Physics-Informed Neural Network Inverse Problems: A Transfer Learning Approach","abstract":"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.","short_abstract":"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 me...","url_abs":"https://arxiv.org/abs/2607.05271","url_pdf":"https://arxiv.org/pdf/2607.05271v1","authors":"[\"Qian Hu\",\"Bin Fan\",\"Yao Xiao\",\"Zhicheng Lin\",\"Meixin Xiong\"]","published":"2026-07-06T16:20:19Z","proceeding":"cs.LG","tasks":"[\"cs.LG\"]","methods":"[\"Diffusion Model\"]","has_code":false}