4 papers
Adaptive Coordinate Transforms for Neural Operators
Chaoyu Liu, Zhonghao Li, Gaohang Chen +5
Neural operators have achieved promising performance on partial differential equations (PDEs), but most existing models are built on fixed Eulerian coordinates. This mismatch betwe…
Generalized Transferable Neural Networks for Steady-State Partial Differential Equations
Tao Cheng, Lili Ju, Zhonghua Qiao +1
Deep learning has emerged as a compelling framework for scientific and engineering computing, motivating growing interest in neural network-based solvers for partial differential e…
A Structure-Preserving Framework for Solving Parabolic Partial Differential Equations with Neural Networks
Gaohang Chen, Lili Ju, Zhonghua Qiao
Solving partial differential equations (PDEs) with neural networks (NNs) has shown great potential in various scientific and engineering fields. However, most existing NN solvers m…
Neural Networks Trained by Weight Permutation are Universal Approximators
Yongqiang Cai, Gaohang Chen, Zhonghua Qiao
The universal approximation property is fundamental to the success of neural networks, and has traditionally been achieved by training networks without any constraints on their par…