21 citations · 69 across the 8 of their papers we have counts for
6 papers · 1 filter
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…
Nonlinear Reduced DNN Models for State Estimation
Wolfgang Dahmen, Min Wang, Zhu Wang
We propose in this paper a data driven state estimation scheme for generating nonlinear reduced models for parametric families of PDEs, directly providing data-to-state maps, repre…
A learning-based projection method for model order reduction of transport problems
Zhichao Peng, Min Wang, Fengyan Li
The Kolmogorov -width of the solution manifolds of transport-dominated problems can decay slowly. As a result, it can be challenging to design efficient and accurate reduced ord…
AsymptoticNG: A regularized natural gradient optimization algorithm with look-ahead strategy
Zedong Tang, Fenlong Jiang, Junke Song +5
Optimizers that further adjust the scale of gradient, such as Adam, Natural Gradient (NG), etc., despite widely concerned and used by the community, are often found poor generaliza…
A Priori Generalization Analysis of the Deep Ritz Method for Solving High Dimensional Elliptic Equations
Jianfeng Lu, Yulong Lu, Min Wang
This paper concerns the a priori generalization analysis of the Deep Ritz Method (DRM) [W. E and B. Yu, 2017], a popular neural-network-based method for solving high dimensional pa…