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

Programming Skills

python: pytorch, jax, tensorflow

julia

matlab

latex

c, c++