5 papers
Nodal Hybrid Neural Solvers for Parametric PDE Systems
Yun Liu, Chen Cui, Shi Shu +1
The numerical solution of partial differential equations (PDEs) is fundamental to scientific and engineering computing. In the presence of strong anisotropy, material heterogeneity…
Projected Sobolev Natural Gradient Descent for Efficient Neural Network Solution of the Gross--Pitaevskii Equation
Chenglong Bao, Chen Cui, Kai Jiang +1
This paper introduces a projected Sobolev natural gradient descent (NGD) method for computing ground states of the Gross--Pitaevskii equation. By projecting a continuous Riemannian…
A Hybrid Iterative Neural Solver Based on Spectral Analysis for Parametric PDEs
Chen Cui, Kai Jiang, Yun Liu +1
Deep learning-based hybrid iterative methods (DL-HIM) have emerged as a promising approach for designing fast neural solvers to tackle large-scale sparse linear systems. DL-HIM com…
A Neural Multigrid Solver for Helmholtz Equations with High Wavenumber and Heterogeneous Media
Chen Cui, Kai Jiang, Shi Shu
In this paper, we propose a deep learning-enhanced multigrid solver for high-frequency and heterogeneous Helmholtz equations. By applying spectral analysis, we categorize the itera…
Momentum-Accelerated Richardson(m) and Their Multilevel Neural Solvers
Zhen Wang, Yun Liu, Chen Cui +1
Recently, designing neural solvers for large-scale linear systems of equations has emerged as a promising approach in scientific and engineering computing. This paper first introdu…