Target-Guided Selective Reweighting for Physics-Informed Neural Network Inverse Problems: A Transfer Learning Approach
This work addresses the negative transfer problem in physics-informed neural networks (PINNs) when applied to inverse problems of partial differential equations (PDEs), where discrepancies in physical mechanisms, parameters, or noise levels between source and target domains degrade performance. To mitigate this, the authors propose TGSR-PINN, which reuses only the network weights from a pre-trained source PINN while independently initializing target-domain physical parameters. The method introduces a novel neuron-level scoring mechanism that combines first-order gradient sensitivity with pre-activation variance to assess neuron relevance. Using a Gaussian mixture model, it generates weak adaptation signals to selectively apply soft attenuation to low-scoring neurons. Experiments demonstrate that TGSR-PINN significantly improves the accuracy of target parameter recovery—without compromising field prediction fidelity—in challenging scenarios including high-Péclet-number convection-diffusion, cross-PDE-family transfer from Allen–Cahn to Burgers equations, and reaction-diffusion tasks with 5% noise.