5 papers · 1 filter
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…
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…
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…
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…