Physics-Informed Foresight Pruning for Sparse PINN Solvers of Nonlinear PDEs

Researchers introduced physics-informed spectrum-aware pruning (PI-SAP), a method that assigns parameter saliency based on PDE residual sensitivity, to create sparse physics-informed neural network (PINN) solvers for nonlinear partial differential equations. In experiments on the Gray-Scott equations, complex Ginzburg-Landau equation, Burgers' equation, and linear convection equation, PI-SAP more consistently preserved Gray-Scott residual fidelity and was competitive under aggressive sparsity, though no pruning criterion proved uniformly optimal across equations or sparsity levels. The study, released as arXiv:2608.25564v1, highlights that residual fidelity, solution accuracy, and kernel conditioning are distinct objectives, motivating pruning methods that balance solution-side and residual-side training dynamics.

arXiv:2608.25564v1 Announce Type: new Abstract: Physics-informed neural networks PINNs often rely on over-parameterized models to optimize coupled solution and differential-residual objectives, leaving unclear how much capacity is necessary and what pruning should preserve. We study foresight pruning at initialization for sparse PirateNet PDE solvers. Standard neural tangent kernel spectrum-aware pruning NTK-SAP aims to preserve output-side training dynamics but may overlook parameters whose main influence arises through derivatives in the governing equations. We introduce physics-informed spectrum-aware pruning PI-SAP , which assigns saliency using sensitivity of the PDE residual. Experiments on the Gray-Scott equations, complex Ginzburg-Landau equation, Burgers' equation, and linear convection equation show that PI-SAP more consistently preserves Gray-Scott residual fidelity and is competitive under aggressive sparsity. However, no criterion is uniformly optimal across equations or sparsity levels. Small-batch PINN-NTK diagnostics further show that residual fidelity, solution accuracy, and kernel conditioning are distinct objectives, motivating pruning methods that explicitly balance solution-side and residual-side training dynamics during optimization.