4 papers
A Structure-Exploiting Implicit-Explicit Trust Region Method for Computing Second-Order Stationary Points of the Landau-Brazovskii Model
Chenglong Bao, Kai Deng, Kai Jiang +1
This work focuses on the reliable computation of second-order stationary points in the high-dimensional nonconvex energy landscape of the Landau-Brazovskii (LB) model, a fundamenta…
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…