1 citations · 2 across the 12 of their papers we have counts for
13 papers
Sparsely connected neural network representation of Lagrange finite element function
Jiaxiong Hao, Yunqing Huang, Nianyu Yi
We construct a mesh-induced sparsely connected neural network framework that exactly reproduces arbitrary-order Lagrange finite element spaces over simplicial meshes. Unlike conven…
DataTransfer: Neural network based interpolation across non-nested meshes
Jiaxiong Hao, Yunqing Huang, Nianyu Yi
In mesh-based numerical simulations, the interpolation of mesh-defined functions across different meshes is a critical task, and achieving high-precision interpolation is of great…
Data-integrated neural networks for solving partial differential equations
Jiachun Zheng, Yunqing Huang, Nianyu Yi +1
In this work, we propose data-integrated neural networks (DataInNet) for solving partial differential equations (PDEs), offering a novel approach to leveraging data (e.g., source t…
Transcending Sparse Measurement Limits: Operator-Learning-Driven Data Super-Resolution for Inverse Source Problem
Guanyu Pan, Jianing Zhou, Xiaotong Liu +2
Inverse source localization from Helmholtz boundary data collected over a narrow aperture is highly ill-posed and severely undersampled, undermining classical solvers (e.g., the Di…
Weights initialization of neural networks for function approximation
Xinwen Hu, Yunqing Huang, Nianyu Yi +1
Neural network-based function approximation plays a pivotal role in the advancement of scientific computing and machine learning. Yet, training such models faces several challenges…
Robust PDE discovery under sparse and highly noisy conditions via attention neural networks
Shilin Zhang, Yunqing Huang, Nianyu Yi +1
The discovery of partial differential equations (PDEs) from experimental data holds great promise for uncovering predictive models of complex physical systems. In this study, we in…
IG-PINNs: Interface-gated physics-informed neural networks for solving elliptic interface problems
Jiachun Zheng, Yunqing Huang, Nianyu Yi
In this work, we develop interface-gated physics-informed neural networks (IG-PINNs) to solve elliptic interface equations. In IG-PINNs, we use a fully connected neural network to…
A posteriori error estimators for fourth order elliptic problems with concentrated loads
Huihui Cao, Yunqing Huang, Nianyu Yi +1
In this paper, we study two residual-based a posteriori error estimators for the interior penalty method in solving the biharmonic equation in a polygonal domain under a conc…
A structure-preserving relaxation Crank-Nicolson finite element method for the Schrödinger-Poisson equation
Huini Liu, Nianyu Yi, Peimeng Yin
In this paper, we propose a mass- and modified energy-conservative relaxation Crank-Nicolson finite element method for the Schrödinger-Poisson equation. Utilizing only a single aux…
Unconditionally energy stable IEQ-FEMs for the Cahn-Hilliard equation and Allen-Cahn equation
Yaoyao Chen, Hailiang Liu, Nianyu Yi +1
In this paper, we present several unconditionally energy-stable invariant energy quadratization (IEQ) finite element methods (FEMs) with linear, first- and second-order accuracy fo…
Recovery type a posteriori error estimation of an adaptive finite element method for Cahn--Hilliard equation
Yaoyao Chen, Yunqing Huang, Nianyu Yi +1
In this paper, we derive a novel recovery type a posteriori error estimation of the Crank-Nicolson finite element method for the Cahn--Hilliard equation. To achieve this, we employ…
An adaptive finite element method for two-dimensional elliptic equations with line Dirac sources
Huihui Cao, Hengguang Li, Nianyu Yi +1
In this paper, we propose a novel adaptive finite element method for an elliptic equation with line Dirac delta functions as a source term. We first study the well-posedness and gl…
Recovery based finite element method for biharmonic equation in two dimensional
Yunqing Huang, Huayi Wei, Wei Yang +1
We design and numerically validate a recovery based linear finite element method for solving the biharmonic equation. The main idea is to replace the gradient operator on…