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math.NA2024
Fully discretized Sobolev gradient flow for the Gross-Pitaevskii eigenvalue problem
Ziang Chen, Jianfeng Lu, Yulong Lu +1
This paper studies the numerical approximation of the ground state of the Gross-Pitaevskii (GP) eigenvalue problem with a fully discretized Sobolev gradient flow induced by the $H^…
math.NA2021★ 7 cited
On the Representation of Solutions to Elliptic PDEs in Barron Spaces
Ziang Chen, Jianfeng Lu, Yulong Lu
Numerical solutions to high-dimensional partial differential equations (PDEs) based on neural networks have seen exciting developments. This paper derives complexity estimates of t…
math.NA2019
Tensor Ring Decomposition: Optimization Landscape and One-loop Convergence of Alternating Least Squares
Ziang Chen, Yingzhou Li, Jianfeng Lu
In this work, we study the tensor ring decomposition and its associated numerical algorithms. We establish a sharp transition of algorithmic difficulty of the optimization problem…