9 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…
Neural network-enhanced -adaptive finite element algorithm for parabolic equations
Jiaxiong Hao, Yunqing Huang, Nianyu Yi +1
In this paper, we propose a novel -adaptive finite element method, enhanced by neural networks, for parabolic equations. The main challenge of the conventional -adaptive fin…
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…