Lizuo Liu (刘栗佐)
不积跬步，无以至千里；不积小流，无以成江海。A journey of one thousand miles can never be made without the accumulation of every single step;An ocean can never be vast without the contribution of every single stream and brook.
Research Interests
• Machine learning algorithms for scientific computing
• Machine learning for causal operators
• Multiscale learning for high dimensional problems, high frequency waves, and fluid dynamics
• Combinations of machine learning algorithms with classical numerical methods
• Mathematical theories of machine learning algorithms
Education
Southern Methodist University
Ph.D, Computational and Applied Mathematics • 2019 — 2023
Advisor: Wei Cai
Shanghai Jiao Tong University
Bachelor of Science, Mathematics and Applied Mathematics • 2014 — 2018
Advisor: Zhenli Xu
Publications
• Preprint
Lizuo Liu, Tongtong Li, Anne Gelb, and Yoonsang Lee, Entropy stable conservative flux form neural networks, arXiv: 2411.01746, 2024
Bo Wang, Heng Yuan, Lizuo Liu, Wenzhong Zhang, and Wei Cai, On the convergence of the multi-scale deep neural network (mscalednn) in approximating oscillatory functions, arXiv: 2212.03416, 2022
Lizuo Liu and Wei Cai, DeepPropNet – A recursive deep propagator neural network for learning evolution PDE operators, arXiv: 2202.13429, 2022
• Journals
Lizuo Liu, Kamaljyoti Nath, and Wei Cai, A causality-deeponet for causal responses of linear dynamical systems, Communications in Computational Physics., 35 (5). 1194-1228, (2024)
Lizuo Liu, Bo Wang, and Wei Cai, Linearized learning methods with multiscale deep neural networks for stationary Navier-Stokes equations with oscillatory solutions, East Asian Journal on Applied Mathematics, 13 (3). 740-758, (2023)
Wei Cai, Xiaoguang Li, and Lizuo Liu, A phase shift deep neural network for high frequency approximation and wave problems, SIAM Journal on Scientific Computing, 42:A3285–A3312, (2020)
Junchao Gao, Franklin Li Duan, Chang Yu, Wentao Meng, Lizuo Liu, Guifu Ding, Congchun Zhang, and Ying Wang., Electrical insulation of ceramic thin film on metallic aero-engine blade for high temperature sensor applications, Ceramics International, 42(16):19269–19275, (2016)
Honors and Awards
SIAM Student Travel Award
Award on SIAM Conference on Mathematics of Data Science, San Diego, CA
September 26 — 30, 2022
2018 Excellent Bachelor Thesis
Award on School of Mathematics Sciences, Shanghai Jiao Tong University
2018
Teaching
• Scientific Computing, Intro to Scientific Computing, Dynamical Systems, Precalculus for Business, Introduction to Proof and Analysis
Teaching Assistant, Department of Mathematics, Southern Methodist University
January, 2019 — May, 2020
Conference Organizations
• Advances in PDE Operator Learning, Minisymposium Co-organizer of the SIAM Conference on Mathematics of Data Science
Atlanta, GA
October 20 - 25, 2024
• Highly Accurate Machine Learning Methods for Solving PDEs, Minisymposium Co-organizer of The third North American High Order Methods Conference
Dartmouth College, Hanover, NH
June 17 — 19, 2024
• Special session co-organizer at the AMS Spring Central Sectional Meeting
Purdue University, West Lafayette, IN
March 26 — 27, 2022
• Minisymposium Co-organizer of the 4th annual meeting of the SIAM Texas-Louisiana section
UTRGV, South Padre Island, TX
November 5 — 7, 2021
• Scientific Machine Learning Paper Reading Group
Department of Mathematics, Southern Methodist University
March, 2020 — December, 2022
Presentations
• DeepPropNet for Learning Non-homogeneous PDEs and Entropy-stable CFN for Hyperbolic Conservation Laws
Atlanta, GA
October 20 - October 25, 2024
• DeepPropNet - A Recursive Deep Neural Network Propagator for Learning Evolutionary PDE Operators
Hanover, NH
June 17- June 19, 2024
• Designing Neural Networks for Hyperbolic Conservation Laws to Predict Entropy Stable Solutions
Newark, NJ
October 20 - October 22, 2023
• Multiscale DNN for Oscillatory Navier-Stokes Flows and Causality in DNN for Dynamic Systems
30 minutes minisymposium, SIAM Conference on Mathematics of Data Science
San Diego, CA
September 26 — 30, 2022
• Learning Causal Operators with DeepPropNet
30 minutes minisymposium, SIAM Conference on Uncertainty Quantification
Atlanta, GA
April 12 — 15, 2022
• Multiscale DNN for Oscillatory Navier-Stokes Flows and Causality in DNN for Dynamic Systems
15 minutes contributed talk, AMS Spring Central Sectional Meeting
Purdue University, West Lafayette, IN
March 26 — 27, 2022
• A Linearized Learning with Multiscale Deep Neural Network for Stationary Navier-Stokes Equations with Oscillatory Solutions
30 minutes minisymposium, 4th Annual Meeting of the SIAM Texas-Louisiana Section
UTRGV, South Padre Island, TX
November 5 — 7, 2021
• Multiscale DNN for Stationary Navier Stokes Equations with Oscillatory Solutions
15 minutes contributed talk, 16th U.S. National Congress on Computational Mechanics
Chicago, IL
July 25 — 29, 2021
• A Phase Shift Deep Neural Network For High Frequency Approximation And Wave Problems
30 minutes minisymposium, 3rd Annual Meeting of the SIAM Texas-Louisiana Section
College Station, TX
October 16 — 18, 2020