most citedUnconditionally energy stable IEQ-FEMs for the Cahn-Hilliard equation and Allen-Cahn equation

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math.NA2025

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…

math.NA2025

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…

math.NA2025

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…

math.NA2025

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…

math.NA2025

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…

math.NA2024

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…