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math.NA2026
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…
math.NA2026
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…