AI 中文总结
针对非线性PDE稀疏PINN求解器，提出PI-SAP剪枝方法，其利用PDE残差灵敏度分配显著性，在高稀疏度下保留Gray-Scott残差保真度，平衡解侧与残差侧训练动态。
AI 中文摘要
物理感知神经网络（PINNs）通常依赖过参数化模型来优化耦合的解与微分残差目标，目前尚不清楚所需的容量以及剪枝应保留的内容。我们研究稀疏PirateNet偏微分方程（PDE）求解器初始化阶段的前瞻性剪枝。标准的神经正切核谱感知剪枝（NTK-SAP）旨在保留输出侧训练动态，但可能忽略那些主要通过控制方程中的导数产生影响的参数。我们引入物理感知谱感知剪枝（PI-SAP），其利用PDE残差的灵敏度来分配显著性。对Gray-Scott方程、复金兹堡-朗道方程、Burgers方程和线性对流方程的实验表明，PI-SAP能更一致地保留Gray-Scott残差保真度，且在高稀疏度下具有竞争力。然而，没有任何准则在所有方程或稀疏度水平上均最优。小批量PINN-NTK诊断进一步显示，残差保真度、解精度和核条件数是不同的目标，这促使剪枝方法在优化过程中明确平衡解侧与残差侧的训练动态。
英文摘要
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.
Comments7 pages, 1 figure, 6 Tables. Submitted to the AI4S 2026 Workshop, Scientific Machine Learning track
