7 papers
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…
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…
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…
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 au…