9 citations · 28 across the 11 of their papers we have counts for
12 papers
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^…
Exact and Efficient Representation of Totally Anti-Symmetric Functions
Ziang Chen, Jianfeng Lu
This paper concerns the long-standing question of representing (totally) anti-symmetric functions in high dimensions. We propose a new ansatz based on the composition of an odd fun…
On the convergence of Sobolev gradient flow for the Gross-Pitaevskii eigenvalue problem
Ziang Chen, Jianfeng Lu, Yulong Lu +1
We study the convergences of three projected Sobolev gradient flows to the ground state of the Gross-Pitaevskii eigenvalue problem. They are constructed as the gradient flows of th…
Representation Theorem for Multivariable Totally Symmetric Functions
Chongyao Chen, Ziang Chen, Jianfeng Lu
In this work, we establish a representation theorem for multivariable totally symmetric functions: a multisymmetric continuous function must be the composition of a continuous func…
On Representing Mixed-Integer Linear Programs by Graph Neural Networks
Ziang Chen, Jialin Liu, Xinshang Wang +2
While Mixed-integer linear programming (MILP) is NP-hard in general, practical MILP has received roughly 100--fold speedup in the past twenty years. Still, many classes of MILPs qu…
On Representing Linear Programs by Graph Neural Networks
Ziang Chen, Jialin Liu, Xinshang Wang +2
Learning to optimize is a rapidly growing area that aims to solve optimization problems or improve existing optimization algorithms using machine learning (ML). In particular, the…
One-dimensional Tensor Network Recovery
Ziang Chen, Jianfeng Lu, Anru R. Zhang
We study the recovery of the underlying graphs or permutations for tensors in the tensor ring or tensor train format. Our proposed algorithms compare the matricization ranks after…
A Regularity Theory for Static Schrödinger Equations on in Spectral Barron Spaces
Ziang Chen, Jianfeng Lu, Yulong Lu +1
Spectral Barron spaces have received considerable interest recently as it is the natural function space for approximation theory of two-layer neural networks with a dimension-free…
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…
On the global convergence of randomized coordinate gradient descent for non-convex optimization
Ziang Chen, Yingzhou Li, Jianfeng Lu
In this work, we analyze the global convergence property of coordinate gradient descent with random choice of coordinates and stepsizes for non-convex optimization problems. Under…
A Trust-Region Method For Nonsmooth Nonconvex Optimization
Ziang Chen, Andre Milzarek, Zaiwen Wen
We propose a trust-region type method for a class of nonsmooth nonconvex optimization problems where the objective function is a summation of a (probably nonconvex) smooth function…
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…