Yiping Lu Research Projects

Undergraduate

Department of Scientific & Engineering Computing
School of mathematical sciences
Peking University
The elite undergraduate training program of School of Mathematical Sciences in Peking University.(Both applied math and pure math track)

Email: luyiping9712 at pku dot edu dot cn
Contact: No. 5 Yiheyuan Road Beijing, 100871 People's Republic of China


Research Overview

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 semi-supervised 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 data-driven 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.
Partial Differential Equations/Control Problem On Graphs.
Generalization Theory Of Deep Learning.

Related Math Fields: Optimal Transport, Optimal Control, Stochastic Analysis, Fourier Analysis

Highlight! Deep Learning And Dynamic Systems

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. "PDE-Net:Learning PDEs From Data",ICML2018

Application:

   
Xiaoshuai Zhang, Yiping Lu, Jaying Liu, Bin Dong. "Dynamically Unfolding Recurrent Restorer: A Moving Endpoint Control Method for Image Restoration", preprint

New! Calculating On Manifold

We want to solve PDE and construte wavelet on manfiold from both spectral and spatral domain.

Image Reconstruction

My main research lies in image processing and reconstruction. Here are projects I'm working on and
  • Nonlocal method and dictionary learning based methods.
  • Unsupervised deep learning based image reconstrction.
  • Manifold learning via PDE(diffusion) and wavelet approximation.
  • (new) PDE based image compression.
Here I listed some of the tasks I am working on.

Sparse Reconstruction

In this project we want to utlize sparse coding to understanding deep learning. The main observation is the similarity between the Relu activation and thresholding. We want to bring the neural network to the sparse field.

Restoration Of Turbulence Destorted Image

Joint work with:Bin Dong, Zhihan Li

In this project we want to restoring a high-quality image from an observed image sequence strongly distorted by atmospheric turbulence. We will utlize no-rigid regestraition and image processing techineque at the same time.

I'm interesting in both deep learning based approach and tradational mathematical modeling methods via PDE.

Blind and real image denoising/reconstrction

Image denoising techniques are traditionally evaluated on images corrupted by known level synthesized i.i.d. Gaussian noise. In this project, we want to extend our model to blind and real image denoising.

   
Xiaoshuai Zhang, Yiping Lu, Jaying Liu, Bin Dong. "Dynamically Unfolding Recurrent Restorer: A Moving Endpoint Control Method for Image Restoration", preprint

Deep Learning Theory

Joint work with:Liwei Wang, Tianle Cai, Siyu Chen

I'm working on generalization theory of deep learning and geometry of the loss surface.

Optimization

I hope I can have some work about optimization one day.

Wavelet And PDE

Joint work with:Bin Dong, Ting Lin

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

Computational Optimal Transport

Joint work with: Justin Solomon.

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.



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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