aiqbench analysis
This research introduces PI-SAP, a novel pruning technique for Physics-Informed Neural Networks (PINNs) that prioritizes PDE residual sensitivity over standard output dynamics. By balancing solution accuracy with differential equation fidelity, the method offers a more robust approach to model compression for solving nonlinear partial differential equations like the Gray-Scott and Burgers' equations. The study highlights that distinct optimization objectives require specialized pruning criteria rather than a single universal standard.
Physics-Informed Foresight Pruning for Sparse PINN Solvers of Nonlinear PDEs
arXiv:2608.25564v1 Announce Type: cross 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.
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.
7 pages, 1 figure, 6 Tables. Submitted to the AI4S 2026 Workshop, Scientific Machine Learning track
Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
arXiv:2608.25564 [cs.LG]
(or arXiv:2608.25564v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2608.25564 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Full text under the publisher's open licence · 263 words
Related coverage
Hybrid quantum-classical physics-informed neural networks for solving nonlinear PDEs: when and where hybridization is effective?
arXiv · Jun 4, 2026
Physics-Informed Residuals for Adaptive Mesh Refinement in Finite-Difference PDE Solvers
arXiv · Jun 8, 2026
Physics-Informed Neural Networks for Complex Eigenfrequency Identification and Mode Structure Reconstruction of the Ground-State ITG Branch
arXiv · Aug 5, 2026
Physics-Informed Stochastic Configuration Machine: A Backpropagation-Free Neural Network with Fast Training for Nonlinear Differential Equations
arXiv · Aug 28, 2026