29 citations · 51 across the 10 of their papers we have counts for
11 papers
Learning Optimal Robust-Pathwise Control of Elliptic Equations with Random Coefficients
Qi Sun, Yanhan Cui, Ling Guo +1
Conventional control approaches to optimization problems under uncertainty entail a practical compromise: deterministic controls offer robustness at the expense of pathwise accurac…
Learning Function-to-Function Mappings: A Fourier Neural Operator for Next-Generation MIMO Systems
Jian Xiao, Ji Wang, Qi Sun +4
Next-generation multiple-input multiple-output (MIMO) systems, characterized by extremely large-scale arrays, holographic surfaces, three-dimensional architectures, and flexible an…
Learning Singularity-Encoded Green's Functions with Application to Iterative Methods
Qi Sun, Shengyan Li, Bowen Zheng +2
Green's function provides an inherent connection between theoretical analysis and numerical methods for elliptic partial differential equations, and general absence of its closed-f…
Lift-and-Embed Learning Methods for Solving Scalar Hyperbolic Equations with Discontinuous Solutions
Qi Sun, Zhenjiang Liu, Lili Ju +1
Deep learning methods, which exploit auto-differentiation to compute derivatives without dispersion or dissipation errors, have recently emerged as a compelling alternative to clas…
Neural Green's Function Accelerated Iterative Methods for Solving Indefinite Boundary Value Problems
Shengyan Li, Qi Sun, Xuejun Xu +1
Neural operators, which learn mappings between the function spaces, have been applied to solve boundary value problems in various ways, including learning mappings from the space o…
Domain Decomposition Learning Methods for Solving Elliptic Problems
Qi Sun, Xuejun Xu, Haotian Yi
With recent advancements in computer hardware and software platforms, there has been a surge of interest in solving partial differential equations with deep learning-based methods,…
A finite element method for two-phase flow with material viscous interface
Maxim Olshanskii, Annalisa Quaini, Qi Sun
This paper studies a model of two-phase flow with an immersed material viscous interface and a finite element method for numerical solution of the resulting system of PDEs. The int…
An unfitted finite element method for two-phase Stokes problems with slip between phases
Maxim Olshanskii, Annalisa Quaini, Qi Sun
We present an isoparametric unfitted finite element approach of the CutFEM or Nitsche-XFEM family for the simulation of two-phase Stokes problems with slip between phases. For the…
Stochastic Training of Residual Networks: a Differential Equation Viewpoint
Qi Sun, Yunzhe Tao, Qiang Du
During the last few years, significant attention has been paid to the stochastic training of artificial neural networks, which is known as an effective regularization approach that…
Nonlocal Neural Networks, Nonlocal Diffusion and Nonlocal Modeling
Yunzhe Tao, Qi Sun, Qiang Du +1
Nonlocal neural networks have been proposed and shown to be effective in several computer vision tasks, where the nonlocal operations can directly capture long-range dependencies i…
Multilevel Monte Carlo Finite Element Method for A Stochastic Optimal Control Problem
Qi Sun, Ju Ming
In this paper, we consider the implementation of multi-level Monte Carlo method to a stochastic optimal control problem with log-normal coefficients and its surrogate model problem…