87 citations · 238 across the 24 of their papers we have counts for
5 papers · 1 filter
Homotopy Relaxation Training Algorithms for Infinite-Width Two-Layer ReLU Neural Networks
Yahong Yang, Qipin Chen, Wenrui Hao
In this paper, we present a novel training approach called the Homotopy Relaxation Training Algorithm (HRTA), aimed at accelerating the training process in contrast to traditional…
Gauss Newton method for solving variational problems of PDEs with neural network discretizaitons
Wenrui Hao, Qingguo Hong, Xianlin Jin
The numerical solution of differential equations using machine learning-based approaches has gained significant popularity. Neural network-based discretization has emerged as a pow…
Companion-Based Multi-Level Finite Element Method for Computing Multiple Solutions of Nonlinear Differential Equations
Wenrui Hao, Sun Lee, Young Ju Lee
The use of nonlinear PDEs has led to significant advancements in various fields, such as physics, biology, ecology, and quantum mechanics. However, finding multiple solutions for n…
HomPINNs: homotopy physics-informed neural networks for solving the inverse problems of nonlinear differential equations with multiple solutions
Haoyang Zheng, Yao Huang, Ziyang Huang +2
Due to the complex behavior arising from non-uniqueness, symmetry, and bifurcations in the solution space, solving inverse problems of nonlinear differential equations (DEs) with m…
Deep Learning via Neural Energy Descent
Wenrui Hao, Chunmei Wang, Xingjian Xu +1
This paper proposes the Nerual Energy Descent (NED) via neural network evolution equations for a wide class of deep learning problems. We show that deep learning can be reformulate…