# Yiping Lu

The long term goal of my research is to develop a hybrid scientific research disipline which combines domain knowledge (differential equation, stochastic process, control,…), machine learning and (randomized) experiments. To this end, I’m working on interdisciplinary research approach across probability and statistics, machine learning, numerical algorithms, control theory, signal processing/inverse problem and operations research.

Here’s my research statement

Here’s my breif bio:

Tenure-Track Assistant professor, Industrial Engineering & Manegement Science, Northwestern University Sep 2024-

Courant Instructor, Courant Institute of Mathematical Sciences, New York University, Sep 2023 - Sep 2024 (expected)

- Ph.D. Candidate, Institute for Computational & Mathematical Engineering, Stanford University, 2019- 2023 (expected)
- advised by Lexing Ying (Math) and Jose Blanchet (Management Science & Enginering).

- B.S. (Honor Track) School of Mathematical Science, Peking University, 2015-2019
- working with Bin Dong and Liwei Wang

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# Research Interest and Highlights

## Debiasing Machine Learning Algorithm for Scientific Computing

1.[*New*] Jose Blanchet, Haoxuan Chen,

Yiping Lu, Lexing Ying. When can Regression-Adjusted Control Variates Help? Rare Events, Sobolev Embedding and Minimax Optimality (alphabetical order)

## Experiment Design

- [*New*]

Yiping Lu, Jiajin Li, Lexing Ying, Jose Blancet. Synthetic Principal Component Design: Fast Covariate Balancing with Synthetic Controls.

## Algorithms and Statistics of Scientific Machine Learning

- [*New*]
Jikai Jin,

Yiping Lu, Jose Blanchet, Lexing Ying Minimax Optimal Kernel Operator Learning via Multilevel Training ICLR 2023

Yiping Lu, Haoxuan Chen, Jianfeng Lu, Lexing Ying, Jose Blanchet. Machine Learning For Elliptic PDEs: Fast Rate Generalization Bound, Neural Scaling Law and Minimax Optimality. International Conference on Learning Representations(ICLR) 2022

Yiping Lu, Jose Blanchet,Lexing Ying. Sobolev Acceleration and Statistical Optimality for Learning Elliptic Equations via Gradient Descent. Neurips 2022- Zichao long
,, Bin Dong. “PDE-Net:Learning PDEs From Data”, Thirty-fifth International Conference on Machine Learning (ICML), 2018Yiping Lu*, Xianzhong Ma

## Robust Machine Learning

Wenlong Ji,

Yiping Lu, et al. An unconstrained layer-peeled perspective on neural collapse. ICLR 2022.Dinghuai Zhang

, Tianyuan Zhang *,equal contribution)Yiping Lu*, Zhanxing Zhu, Bin Dong. “You Only Propagate Once: Painless Adversarial Training Using Maximal Principle.” 33rd Annual Conference on Neural Information Processing Systems (NeurIPS) 2019 (- [*New*]

Yiping Lu, Wenlong Ji, Zach Izzo, et al. Importance Tempering: Group Robustness for Overparameterized Models. arXiv preprint arXiv:2209.08745, 2022.

## Optimal Control Formulation of Deep Learning

Yiping Lu, Chao Ma, Yulong Lu, Jianfeng Lu, Lexing Ying. “A Mean-field Analysis of Deep ResNet and Beyond: Towards Provable Optimization Via Overparameterization From Depth” Thirty-seventh International Conference on Machine Learning (ICML), 2020Dinghuai Zhang

, Tianyuan Zhang *,equal contribution)Yiping Lu*, Zhanxing Zhu, Bin Dong. “You Only Propagate Once: Painless Adversarial Training Using Maximal Principle.” 33rd Annual Conference on Neural Information Processing Systems (NeurIPS) 2019 (

Yiping Lu, Aoxiao Zhong *, Quanzheng Li, Bin Dong. “Beyond Finite Layer Neural Network:Bridging Deep Architects and Numerical Differential Equations” Thirty-fifth International Conference on Machine Learning (ICML), 2018 (equal contribution)

## Inverse Problem and Image Processing

Xiaoshuai Zhang

,equal contribution)Yiping Lu*, Jiaying Liu, Bin Dong. “Dynamically Unfolding Recurrent Restorer: A Moving Endpoint Control Method for Image Restoration” Seventh International Conference on Learning Representations(ICLR) 2019(Bin Dong, Haochen Ju,

Yiping Lu, Zuoqiang Shi. “ CURE: Curvature Regularization For Missing Data Recovery.” SIAM Journal on Imaging Science, 13(4), 2169-2188, 2020 (alphabetical order)

My Erdos Number = 4

Yiping Lu -> Lexing Ying -> David L. Donoho -> Charles Kam-tai Chui -> Paul Erdős

Yiping Lu -> Jose H. Blanchet -> Martin I. Reiman -> Fan Chung -> Paul Erdős