16 citations · 63 across the 16 of their papers we have counts for
16 papers
Elliptic interface problem approximated by CutFEM: I. Conservative flux recovery and numerical validation of adaptive mesh refinement
Daniela Capatina, Aimene Gouasmi, Cuiyu He
We study an elliptic interface problem with discontinuous diffusion coefficients on unfitted meshes using the CutFEM method. Our main contribution is the reconstruction of conserva…
NODE-AdvGAN: Improving the transferability and perceptual similarity of adversarial examples by dynamic-system-driven adversarial generative model
Xinheng Xie, Yue Wu, Cuiyu He
Understanding adversarial examples is crucial for improving model robustness, as they introduce imperceptible perturbations to deceive models. Effective adversarial examples, there…
Best approximation results and essential boundary conditions for novel types of weak adversarial network discretizations for PDEs
Silvia Bertoluzza, Erik Burman, Cuiyu He
In this paper, we provide a theoretical analysis of the recently introduced weakly adversarial networks (WAN) method, used to approximate partial differential equations in high dim…
NODE-ImgNet: a PDE-informed effective and robust model for image denoising
Xinheng Xie, Yue Wu, Hao Ni +1
Inspired by the traditional partial differential equation (PDE) approach for image denoising, we propose a novel neural network architecture, referred as NODE-ImgNet, that combines…
p-Adic Statistical Field Theory and Convolutional Deep Boltzmann Machines
W. A. Zúñiga-Galindo, Cuiyu He, B. A. Zambrano-Luna
Understanding how deep learning architectures work is a central scientific problem. Recently, a correspondence between neural networks (NNs) and Euclidean quantum field theories (Q…
Towards fast weak adversarial training to solve high dimensional parabolic partial differential equations using XNODE-WAN
Paul Valsecchi Oliva, Yue Wu, Cuiyu He +1
Due to the curse of dimensionality, solving high dimensional parabolic partial differential equations (PDEs) has been a challenging problem for decades. Recently, a weak adversaria…
Optimal Control of Convection-Cooling and Numerical Implementation
Cuiyu He, Weiwei Hu, Lin Mu
This paper is concerned with the problem of enhancing convection-cooling via active control of the incompressible velocity field, described by a stationary diffusion-convection mod…
Comparison of Shape Derivatives using CutFEM for Ill-posed Bernoulli Free Boundary Problem
Erik Burman, Cuiyu He, Mats G. Larson
In this paper we discuss a level set approach for the identification of an unknown boundary in a computational domain. The problem takes the form of a Bernoulli problem where only…
An a posteriori error estimate of the outer normal derivative using dual weights
Silvia Bertoluzza, Erik Burman, Cuiyu He
We derive a residual based a-posteriori error estimate for the outer normal flux of approximations to {the diffusion problem with variable coefficient}. By analyzing the solution o…
Generalized Prager-Synge Inequality and Equilibrated Error Estimators for Discontinuous Elements
Cuiyu He, Zhiqiang Cai, Shun Zhang
The well-known Prager-Synge identity is valid in and serves as a foundation for developing equilibrated a posteriori error estimators for continuous elements. In this pape…
Residual-based a posteriori error estimation for immersed finite element methods
Cuiyu He, Xu Zhang
In this paper we introduce and analyze the residual-based a posteriori error estimation of the partially penalized immersed finite element method for solving elliptic interface pro…
A Posteriori Error Estimates with Boundary Correction for a Cut Finite Element Method
Erik Burman, Cuiyu He, Mats G. Larson
In this work we study a residual based a posteriori error estimation for the CutFEM method applied to an elliptic model problem. We consider the problem with non-polygonal boundary…
Primal dual mixed finite element methods for indefinite advection--diffusion equations
Erik Burman, Cuiyu He
We consider primal-dual mixed finite element methods for the advection--diffusion equation. For the primal variable we use standard continuous finite element space and for the flux…
Residual-based a Posteriori Error Estimate for Interface Problems: Nonconforming Linear Elements
Zhiqiang Cai, Cuiyu He, Shun Zhang
In this paper, we study a modified residual-based a posteriori error estimator for the nonconforming linear finite element approximation to the interface problem. The reliability o…
Finite Element Methods for Interface Problems: Robust Residual-Based A Posteriori Error Estimates
Zhiqiang Cai, Cuiyu He, Shun Zhang
For elliptic interface problems, this paper studies residual-based a posteriori error estimations for various finite element approximations. For the conforming and the Raviart-Thom…
Improved ZZ A Posteriori Error Estimators for Diffusion Problems: Conforming Linear Elements
Zhiqiang Cai, Cuiyu He, Shun Zhang
In \cite{CaZh:09}, we introduced and analyzed an improved Zienkiewicz-Zhu (ZZ) estimator for the conforming linear finite element approximation to elliptic interface problems. The…