540 citations · 908 across the 23 of their papers we have counts for
24 papers
Laplace-fPINNs: Laplace-based fractional physics-informed neural networks for solving forward and inverse problems of subdiffusion
Xiong-Bin Yan, Zhi-Qin John Xu, Zheng Ma
The use of Physics-informed neural networks (PINNs) has shown promise in solving forward and inverse problems of fractional diffusion equations. However, due to the fact that autom…
Bayesian Inversion with Neural Operator (BINO) for Modeling Subdiffusion: Forward and Inverse Problems
Xiong-bin Yan, Zhi-Qin John Xu, Zheng Ma
Fractional diffusion equations have been an effective tool for modeling anomalous diffusion in complicated systems. However, traditional numerical methods require expensive computa…
GEDI: A Graph-based End-to-end Data Imputation Framework
Katrina Chen, Xiuqin Liang, Zheng Ma +1
Data imputation is an effective way to handle missing data, which is common in practical applications. In this study, we propose and test a novel data imputation process that achie…
Asymptotic-Preserving Neural Networks for Multiscale Time-Dependent Linear Transport Equations
Shi Jin, Zheng Ma, Keke Wu
In this paper we develop a neural network for the numerical simulation of time-dependent linear transport equations with diffusive scaling and uncertainties. The goal of the networ…
MOD-Net: A Machine Learning Approach via Model-Operator-Data Network for Solving PDEs
Lulu Zhang, Tao Luo, Yaoyu Zhang +3
In this paper, we propose a a machine learning approach via model-operator-data network (MOD-Net) for solving PDEs. A MOD-Net is driven by a model to solve PDEs based on operator r…
An Upper Limit of Decaying Rate with Respect to Frequency in Deep Neural Network
Tao Luo, Zheng Ma, Zhiwei Wang +2
Deep neural network (DNN) usually learns the target function from low to high frequency, which is called frequency principle or spectral bias. This frequency principle sheds light…
Network Pruning via Resource Reallocation
Yuenan Hou, Zheng Ma, Chunxiao Liu +2
Channel pruning is broadly recognized as an effective approach to obtain a small compact model through eliminating unimportant channels from a large cumbersome network. Contemporar…
Linear Frequency Principle Model to Understand the Absence of Overfitting in Neural Networks
Yaoyu Zhang, Tao Luo, Zheng Ma +1
Why heavily parameterized neural networks (NNs) do not overfit the data is an important long standing open question. We propose a phenomenological model of the NN training to expla…
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…
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…
Path Integral Based Convolution and Pooling for Graph Neural Networks
Zheng Ma, Junyu Xuan, Yu Guang Wang +2
Graph neural networks (GNNs) extends the functionality of traditional neural networks to graph-structured data. Similar to CNNs, an optimized design of graph convolution and poolin…
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…
Inter-Region Affinity Distillation for Road Marking Segmentation
Yuenan Hou, Zheng Ma, Chunxiao Liu +2
We study the problem of distilling knowledge from a large deep teacher network to a much smaller student network for the task of road marking segmentation. In this work, we explore…
Defending from adversarial examples with a two-stream architecture
Hao Ge, Xiaoguang Tu, Mei Xie +1
In recent years, deep learning has shown impressive performance on many tasks. However, recent researches showed that deep learning systems are vulnerable to small, specially craft…
Haar Graph Pooling
Yu Guang Wang, Ming Li, Zheng Ma +3
Deep Graph Neural Networks (GNNs) are useful models for graph classification and graph-based regression tasks. In these tasks, graph pooling is a critical ingredient by which GNNs…
Learning Lightweight Lane Detection CNNs by Self Attention Distillation
Yuenan Hou, Zheng Ma, Chunxiao Liu +1
Training deep models for lane detection is challenging due to the very subtle and sparse supervisory signals inherent in lane annotations. Without learning from much richer context…
Fast Haar Transforms for Graph Neural Networks
Ming Li, Zheng Ma, Yu Guang Wang +1
Graph Neural Networks (GNNs) have become a topic of intense research recently due to their powerful capability in high-dimensional classification and regression tasks for graph-str…
Theory of the Frequency Principle for General Deep Neural Networks
Tao Luo, Zheng Ma, Zhi-Qin John Xu +1
Along with fruitful applications of Deep Neural Networks (DNNs) to realistic problems, recently, some empirical studies of DNNs reported a universal phenomenon of Frequency Princip…
Explicitizing an Implicit Bias of the Frequency Principle in Two-layer Neural Networks
Yaoyu Zhang, Zhi-Qin John Xu, Tao Luo +1
It remains a puzzle that why deep neural networks (DNNs), with more parameters than samples, often generalize well. An attempt of understanding this puzzle is to discover implicit…
A type of generalization error induced by initialization in deep neural networks
Yaoyu Zhang, Zhi-Qin John Xu, Tao Luo +1
How initialization and loss function affect the learning of a deep neural network (DNN), specifically its generalization error, is an important problem in practice. In this work, b…
PAN: Path Integral Based Convolution for Deep Graph Neural Networks
Zheng Ma, Ming Li, Yuguang Wang
Convolution operations designed for graph-structured data usually utilize the graph Laplacian, which can be seen as message passing between the adjacent neighbors through a generic…
Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks
Zhi-Qin John Xu, Yaoyu Zhang, Tao Luo +2
We study the training process of Deep Neural Networks (DNNs) from the Fourier analysis perspective. We demonstrate a very universal Frequency Principle (F-Principle) -- DNNs often…
NADPEx: An on-policy temporally consistent exploration method for deep reinforcement learning
Sirui Xie, Junning Huang, Lanxin Lei +4
Reinforcement learning agents need exploratory behaviors to escape from local optima. These behaviors may include both immediate dithering perturbation and temporally consistent ex…
Learning to Steer by Mimicking Features from Heterogeneous Auxiliary Networks
Yuenan Hou, Zheng Ma, Chunxiao Liu +1
The training of many existing end-to-end steering angle prediction models heavily relies on steering angles as the supervisory signal. Without learning from much richer contexts, t…