Target-Guided Selective Reweighting for Physics-Informed Neural Network Inverse Problems: A Transfer Learning Approach
2026-07-06 • Machine Learning
Machine Learning
AI summaryⓘ
The authors address challenges in using physics-informed neural networks (PINNs) to solve inverse problems in partial differential equations, where transferring knowledge from one task to another can lead to errors in key parameters. They propose a method called TGSR-PINN that carefully adjusts only parts of the neural network based on how important each neuron is for the new task, avoiding harmful changes. Their approach improves the recovery of physical parameters without losing accuracy in predicting the physical fields, as shown in several tests with different PDE problems. They also show that different components of their method each play a role in its success.
Physics-informed neural networksPartial differential equationsInverse problemsTransfer learningParameter recoveryNeuron sensitivityGaussian mixture modelAdvection-diffusion equationAllen–Cahn equationBurgers equation
Authors
Qian Hu, Bin Fan, Yao Xiao, Zhicheng Lin, Meixin Xiong
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.