提出新剪枝方法，让物理信息神经网络更高效求解非线性偏微分方程。
Physics-Informed Foresight Pruning for Sparse PINN Solvers of Nonlinear PDEs
- 基于物理残差敏感性设计剪枝准则，保留对方程约束关键的参数。
- 在灰-斯科特等方程上，剪枝后残差保真度更稳定，极端稀疏下仍有效。
- 揭示了求解精度与残差拟合是不同目标，适合追求效率的偏微分方程求解者。
物理信息神经网络（PINNs）常依赖过参数化模型以优化解与微分残差的联合目标，但难以确定所需容量及应保留哪些参数。本文研究初始阶段的前瞻剪枝，针对稀疏PirateNet PDE求解器。标准神经正切核谱感知剪枝（NTK-SAP）关注输出端训练动态，可能忽略通过控制方程导数起作用的关键参数。为此，我们提出物理信息谱感知剪枝（PI-SAP），基于对PDE残差的敏感性分配参数重要性。在灰-斯科特方程、复高兹堡-朗道方程、伯格斯方程和线性对流方程上的实验表明，PI-SAP在保持灰-斯科特方程残差保真度方面更一致，在高稀疏度下也具竞争力。然而，无单一准则在所有方程或稀疏水平上始终最优。小批量PINN-NTK诊断进一步显示，残差保真度、解精度与核条件数是独立目标，提示应在优化中显式平衡解端与残差端的训练动态。
原文摘要 · Abstract (English)
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.
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