540 citations · 833 across the 33 of their papers we have counts for
5 papers · 1 filter
Fourier-domain Variational Formulation and Its Well-posedness for Supervised Learning
Tao Luo, Zheng Ma, Zhiwei Wang +2
A supervised learning problem is to find a function in a hypothesis function space given values on isolated data points. Inspired by the frequency principle in neural networks, we…
A deep learning-based ODE solver for chemical kinetics
Tianhan Zhang, Yaoyu Zhang, Weinan E +1
Developing efficient and accurate algorithms for chemistry integration is a challenging task due to its strong stiffness and high dimensionality. The current work presents a deep l…
On the exact computation of linear frequency principle dynamics and its generalization
Tao Luo, Zheng Ma, Zhi-Qin John Xu +1
Recent works show an intriguing phenomenon of Frequency Principle (F-Principle) that deep neural networks (DNNs) fit the target function from low to high frequency during the train…
Phase diagram for two-layer ReLU neural networks at infinite-width limit
Tao Luo, Zhi-Qin John Xu, Zheng Ma +1
How neural network behaves during the training over different choices of hyperparameters is an important question in the study of neural networks. In this work, inspired by the pha…
Implicit bias with Ritz-Galerkin method in understanding deep learning for solving PDEs
Jihong Wang, Zhi-Qin John Xu, Jiwei Zhang +1
This paper aims at studying the difference between Ritz-Galerkin (R-G) method and deep neural network (DNN) method in solving partial differential equations (PDEs) to better unders…