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

arXiv:2607.05271v2 Announce Type: replace 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 short target 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-P\'{e}clet 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.

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 short target 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.

Machine Learning (cs.LG)

arXiv:2607.05271 [cs.LG]

(or arXiv:2607.05271v2 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2607.05271 Focus to learn more arXiv-issued DOI via DataCite

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

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