4 papers
Learning Laplacian Eigenspace with Mass-Aware Neural Operators on Point Clouds
Zherui Yang, Tao Du, Ligang Liu
The eigendecomposition of the Laplace--Beltrami Operator (LBO) is fundamental to geometric analysis, yet computing its low-frequency eigenmodes remains a significant bottleneck due…
Simple yet Effective: Low-Rank Spatial Attention for Neural Operators
Zherui Yang, Haiyang Xin, Tao Du +1
Neural operators have emerged as data-driven surrogates for solving partial differential equations (PDEs), and their success hinges on efficiently modeling the long-range, global c…
Learning Sparse Approximate Inverse Preconditioners for Conjugate Gradient Solvers on GPUs
Zherui Yang, Zhehao Li, Kangbo Lyu +3
The conjugate gradient solver (CG) is a prevalent method for solving symmetric and positive definite linear systems Ax=b, where effective preconditioners are crucial for fast conve…
SUPRA: Subspace Parameterized Attention for Neural Operator on General Domains
Zherui Yang, Zhengyang Xue, Ligang Liu
Neural operators are efficient surrogate models for solving partial differential equations (PDEs), but their key components face challenges: (1) in order to improve accuracy, atten…