Dynamic Gaussian Graph Operator: Learning parametric partial differential equations in arbitrary discrete mechanics problems

arXiv:2403.02810v1 Announce Type: new
Abstract: Deep learning methods have access to be employed for solving physical systems governed by parametric partial differential equations (PDEs) due to massive scientific data. It has been refined to operator learning that focuses on learning non-linear mapping between infinite-dimensional function spaces, offering interface from observations to solutions. However, state-of-the-art neural operators are limited to constant and uniform discretization, thereby leading to deficiency in generalization on arbitrary discretization schemes for computational domain. In this work, we …

abstract arxiv cs.ai cs.lg data deep learning differential dynamic function graph linear mapping massive non-linear parametric spaces systems type