155 citations · 379 across the 24 of their papers we have counts for
11 papers · 1 filter
Neural Flow Operators can Approximate any Operator: Abstract Frameworks and Universal Approximations
Shuang Chen, Juncai He, Xue-Cheng Tai
We introduce an abstract neural flow framework for neural networks and neural operators. The framework contains two continuous-depth models, namely neural flows with composition an…
Self-composing neural operators for high-frequency and multiscale PDE surrogates
Juncai He, Xinliang Liu, Jinchao Xu
Addressing the computational challenges of high-frequency and multiscale partial differential equations (PDEs), this work introduces a self-composing neural operator (SC-NO) framew…
Expressivity and Approximation Properties of Deep Neural Networks with ReLU Activation
Juncai He, Tong Mao, Jinchao Xu
In this paper, we investigate the expressivity and approximation properties of deep neural networks employing the ReLU activation function for . Although deep ReLU ne…
MgNO: Efficient Parameterization of Linear Operators via Multigrid
Juncai He, Xinliang Liu, Jinchao Xu
In this work, we propose a concise neural operator architecture for operator learning. Drawing an analogy with a conventional fully connected neural network, we define the neural o…
On the Optimal Expressive Power of ReLU DNNs and Its Application in Approximation with Kolmogorov Superposition Theorem
Juncai He
This paper is devoted to studying the optimal expressive power of ReLU deep neural networks (DNNs) and its application in approximation via the Kolmogorov Superposition Theorem. We…
Linear Regression on Manifold Structured Data: the Impact of Extrinsic Geometry on Solutions
Liangchen Liu, Juncai He, Richard Tsai
In this paper, we study linear regression applied to data structured on a manifold. We assume that the data manifold is smooth and is embedded in a Euclidean space, and our objecti…
An Enhanced V-cycle MgNet Model for Operator Learning in Numerical Partial Differential Equations
Jianqing Zhu, Juncai He, Qiumei Huang
This study used a multigrid-based convolutional neural network architecture known as MgNet in operator learning to solve numerical partial differential equations (PDEs). Given the…
Side Effects of Learning from Low-dimensional Data Embedded in a Euclidean Space
Juncai He, Richard Tsai, Rachel Ward
The low-dimensional manifold hypothesis posits that the data found in many applications, such as those involving natural images, lie (approximately) on low-dimensional manifolds em…
A Weight Initialization Based on the Linear Product Structure for Neural Networks
Qipin Chen, Wenrui Hao, Juncai He
Weight initialization plays an important role in training neural networks and also affects tremendous deep learning applications. Various weight initialization strategies have alre…
Approximation Properties of Deep ReLU CNNs
Juncai He, Lin Li, Jinchao Xu
This paper focuses on establishing approximation properties for deep ReLU convolutional neural networks (CNNs) in two-dimensional space. The analysis is based on a decomposit…
Make Regularization Effective in Training Sparse CNN
Juncai He, Xiaodong Jia, Jinchao Xu +2
Compressed Sensing using regularization is among the most powerful and popular sparsification technique in many applications, but why has it not been used to obtain sparse…