A new arXiv preprint examines why physics-informed neural networks (PINNs) and their Kolmogorov-Arnold counterparts (PIKANs) often fail when used with domain decomposition to solve partial differential equations over complex geometries. The authors attribute these problems to conflicting gradient signals and propose a conflict-free gradient approach to improve training stability and scalability.
A new arXiv paper argues that physics-informed neural networks can match target function values while still producing inaccurate derivatives. The authors describe this as a distinct failure mode and provide strengthened benchmark evidence for it, based on models trained only on function values. The work suggests that evaluating PINNs by function agreement alone can mask errors in the derivative terms central to solving differential equations.
A new arXiv paper proposes a pullback-corrected scalar auxiliary variable (PB-SAV) optimizer that adds momentum and adaptive mobility. The method is aimed at scientific machine learning objectives that combine several loss terms, such as the residual, boundary, initial, and data losses used in physics-informed neural networks. The abstract frames the work as addressing optimization challenges specific to these composite objectives.
A new arXiv paper introduces PhysSAE, a method that applies sparse autoencoders to inspect what hidden layers in physics-informed neural networks actually represent. The authors aim to determine whether these networks learn localized, physically meaningful features tied to the PDE residuals they are trained on. The work falls within mechanistic interpretability research for scientific machine learning.
A new arXiv paper introduces 3GAS-PINNs, a variant of physics-informed neural networks that uses gradient-guided Gaussian adaptive sampling to place collocation points. The method targets common weaknesses in PINNs on nonlinear partial differential equations, such as slow convergence, gradient imbalance, and poor resolution of demanding regions. By concentrating sampling where it matters most, the approach aims to improve training efficiency and solution accuracy.