565 citations · 1.5k across the 34 of their papers we have counts for
34 papers
Meta-Auto-Decoder: A Meta-Learning Based Reduced Order Model for Solving Parametric Partial Differential Equations
Zhanhong Ye, Xiang Huang, Hongsheng Liu +1
Many important problems in science and engineering require solving the so-called parametric partial differential equations (PDEs), i.e., PDEs with different physical parameters, bo…
Trained Model in Supervised Deep Learning is a Conditional Risk Minimizer
Yutong Xie, Dufan Wu, Bin Dong +1
We proved that a trained model in supervised deep learning minimizes the conditional risk for each input (Theorem 2.1). This property provided insights into the behavior of trained…
Layer-Parallel Training of Residual Networks with Auxiliary-Variable Networks
Qi Sun, Hexin Dong, Zewei Chen +3
Gradient-based methods for the distributed training of residual networks (ResNets) typically require a forward pass of the input data, followed by back-propagating the error gradie…
Solving Partial Differential Equations with Point Source Based on Physics-Informed Neural Networks
Xiang Huang, Hongsheng Liu, Beiji Shi +11
In recent years, deep learning technology has been used to solve partial differential equations (PDEs), among which the physics-informed neural networks (PINNs) emerges to be a pro…
Meta-Auto-Decoder for Solving Parametric Partial Differential Equations
Xiang Huang, Zhanhong Ye, Hongsheng Liu +11
Many important problems in science and engineering require solving the so-called parametric partial differential equations (PDEs), i.e., PDEs with different physical parameters, bo…
Learning invariance preserving moment closure model for Boltzmann-BGK equation
Zhengyi Li, Bin Dong, Yanli Wang
As one of the main governing equations in kinetic theory, the Boltzmann equation is widely utilized in aerospace, microscopic flow, etc. Its high-resolution simulation is crucial i…