155 citations · 379 across the 24 of their papers we have counts for
5 papers · 1 filter
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…
FV-MgNet: Fully Connected V-cycle MgNet for Interpretable Time Series Forecasting
Jianqing Zhu, Juncai He, Lian Zhang +1
By investigating iterative methods for a constrained linear model, we propose a new class of fully connected V-cycle MgNet for long-term time series forecasting, which is one of th…
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…