Problem
Research questions and friction points this paper is trying to address.
Physics-Informed Neural Networks
Pruning
Nonlinear PDEs
Sensitivity
Sparse Solvers
Physics-Informed Foresight Pruning for Sparse PINN Solvers of Nonlinear PDEs
🤖 AI Summary
研究提出了一种基于物理信息的谱感知剪枝方法（PI-SAP），以提高稀疏PINN求解非线性PDE时的性能，通过保留对PDE残差敏感的参数来优化模型。
📝 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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Physics-informed spectrum-aware pruning
PI-SAP
Sparse PINN solvers
PDE residual fidelity
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