5 papers
Prescribed-Basis Coefficient-to-Coefficient Neural Operator for Partial Differential Equations
Chuqi Chen, Yang Xiang, Weihong Zhang
Operator learning provides a data-driven approach to approximating solution operators of partial differential equations, but its effectiveness depends strongly on how input and out…
Investigating amorphization as a deformation mechanism using a novel phase field model at the mesoscale
Yuntong Huang, Shuyang Dai, Chuqi Chen +1
Amorphization during severe plastic deformation has been observed in various crystalline materials, yet its underlying mechanisms remain poorly understood. This study introduces a…
Learn Singularly Perturbed Solutions via Homotopy Dynamics
Chuqi Chen, Yahong Yang, Yang Xiang +1
Solving partial differential equations (PDEs) using neural networks has become a central focus in scientific machine learning. Training neural networks for singularly perturbed pro…
Automatic Differentiation is Essential in Training Neural Networks for Solving Differential Equations
Chuqi Chen, Yahong Yang, Yang Xiang +1
Neural network-based approaches have recently shown significant promise in solving partial differential equations (PDEs) in science and engineering, especially in scenarios featuri…
Quantifying Training Difficulty and Accelerating Convergence in Neural Network-Based PDE Solvers
Chuqi Chen, Qixuan Zhou, Yahong Yang +2
Neural network-based methods have emerged as powerful tools for solving partial differential equations (PDEs) in scientific and engineering applications, particularly when handling…