Parametric Encoding with Attention and Convolution Mitigate Spectral Bias of Neural Partial Differential Equation Solvers

arXiv:2403.15652v1 Announce Type: new
Abstract: Deep neural networks (DNNs) are increasingly used to solve partial differential equations (PDEs) that naturally arise while modeling a wide range of systems and physical phenomena. However, the accuracy of such DNNs decreases as the PDE complexity increases and they also suffer from spectral bias as they tend to learn the low-frequency solution characteristics. To address these issues, we introduce Parametric Grid Convolutional Attention Networks (PGCANs) that can solve PDE systems without leveraging any labeled …

abstract accuracy arxiv attention bias complexity convolution cs.lg differential differential equation encoding equation however modeling networks neural networks parametric solve systems type