Yiping Lu Research ProjectsUndergraduate
Department of Scientific & Engineering Computing


If you are interested in any problem that I'm working on or related, please contact me! I'm look forward to potential collaborators.
I'm interested in all computational and statistical methods used in imaging and graphics. Now I am working on data scince, hoping to build the bridge between deep learning and PDE(variation), wavelets and other traditional data analysis methods. Although I'm not major in statistics or computer science, I interested in statical learning theroy applied in artificial intelligence. I am also working on learning on manifolds, mainly semisupervised learning via diffusion or wavelets. At the same time, we want to bring insight to graph CNN designing.
At a high level, my research aim to combine the data driven method with model based methods. Before the uprise of deep learning methods, people need first to design a mathematical model to describe the physic laws behind the problem. My dream is to converge this two methodologies which can build great predictive performance datadriven model with theoretical guarantee.
I am also working on learning theory, uncertainty quantification, sparse coding, inverse problem and computer vision.
Research Area:
(Stochastic) Dynamic System View Of Deep Learning. 
Computational Tools For Imaging And Graphics 
Sparse Representation And Dictionary Learning Of Images.  
Geometric Partial Differential Equations/Control Problem On Graphs.  
Kernel Learning, Nonlocal PDE, Gaussian Process and Deep Learning. 
Related Math Fields: Optimal Transport, Optimal Control, Stochastic Analysis, Fourier Analysis
Joint work with: Bin Dong, Zichao Long, Xianzhong Ma, Aoxiao Zhong
In this project we want to bridge dynamic control theory and deep learning.
First we utlize the neural network to learn a dynamic. We want to learn the PDE and the numerical scheme of the PDE at the same time. In this method, we take both interpretability and predictability in to consider.
Secondly we are also interesting in utlize the differential equation to analysis the deep neural network. Not only utilizing the algorithms from control problems but also want to do some theorical works to analysis the property of th neural network. At the same time, we also working on the relationship with boosting algorithms.
I'm also interested in utlizing (stochastic) dynamic system to anlaysis optimization problems. Here is a chinese brief introduction I write on zhihu link and here is a report I wrote on this topic pdf.
Yiping Lu, Aoxiao Zhong, Quanzheng Li, Bin Dong. "Beyond Finite Layer Neural Network:Bridging Deep Architects and Numerical Differential Equations" ICML2018 
Zichao long, Yiping Lu, Xianzhong Ma, Bin Dong. "PDENet:Learning PDEs From Data",ICML2018 
Xiaoshuai Zhang, Yiping Lu, Jiaying Liu, Bin Dong. "Dynamically Unfolding Recurrent Restorer: A Moving Endpoint Control Method for Image Restoration",ICLR2019 
Zichao long, Yiping Lu, Bin Dong. "PDENet2.0:Learning PDEs from Data with A NumericSymbolic Hybrid Deep Network",Submitted 
We want to solve PDE and construte wavelet on manfiold from both spectral and spatral domain.
Image Inpainting: WNLL:27.78dB, WeCURE: 28.56dB
Semisupervised Learning:
Bin Dong, Haochen Ju, Yiping Lu, Zuoqiang Shi. "CURE: Curvature Regularization For Missing Data Recovery." Submitted 
My main research lies in image processing and reconstruction. Here are projects I'm working on and
I'm interesting in both deep learning based approach and tradational mathematical modeling methods via PDE and sparse representation.
I'm interested in image blind debluring, image compression and image editting.
Xiaoshuai Zhang, Yiping Lu, Jaying Liu, Bin Dong. "Dynamically Unfolding Recurrent Restorer: A Moving Endpoint Control Method for Image Restoration", preprint 
Joint work with:Liwei Wang, Tianle Cai, Siyu Chen
I'm working on generalization theory of deep learning and geometry of the loss surface.
I'm also curious about infinte width neural network, i.e. mean field limit. I believe the mean field limit has a deep connection with the kernel learning.
I hope I can have some work about optimization one day.
To utilize the sparsity of wavelet representation of the functions in the sobolev space, we want to utlize the wavelet to propose a TVD scheme to capture the shock without tracking it.
I'm also interested in the relationship between wavelet based models and PDE/variation based models in imaging analysis. I'm working on the relationship between the edge calculated by wavelet based methods and PDE/variation methods.
Estimating the jumpset by ell_0 norm minimization (The test image is Ogino Yuka from NGT48)
Wavelet Based PDE Solver
Optimal transport is a math field first bulid in pure math. Recent years, it has raised wide attention in imaging science, machine learning and finance.
I'm working on: fast algorithm for sparse transport, barycenter.
Theory without practice is empty, but equally, practice without theory is blind.  I. Kant
People who wish to analyze nature without using mathematics must settle for a reduced understanding.  Richard Feynman