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

2026-07-06

AI Summary

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.

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.

Problem

• Physics-Informed Neural Networks
• Inverse Problems
• Transfer Learning
• Negative Transfer
• Parameter Recovery

Innovation

• Physics-Informed Neural Networks
• Transfer Learning
• Selective Reweighting
• Inverse Problems
• Target-Guided Adaptation