avatar

Shanqing Liu

Postdoc researcher
Division of Applied Mathematics, Brown University
shanqing_liu[at]brown[dot]edu


About Me

Starting from Feb. 2024, I am a Post-doc Research Associate at Division of Applied Mathematics , Brown University, where I am part of CRUNCH group. I got my Ph.D. at Centre de Mathématiques Appliquées de l'Ecole Polytechnique (CMAP), where I was part of TROPICAL Team.

Research Interests

I study optimal control and optimization in my Ph.D., with a focus on the Dynamic Programming Principle and the Hamilton-Jacobi-Bellman (HJB) equations. My research involves developing numerical schemes to address the curse of dimensionality.

I have also worked broadly on numerical methods for optimal control and optimization, as well as on the design of efficient numerical solvers for partial differential equations (PDEs).

More recently, my interests have shifted toward the intersection of optimization and challenges in scientific machine learning.

Bio

Publications

Preprint

  1. [p1] A Physics-Informed Symplectic Operator Network for Real-Time Optimal Control of Multi-Agent Systems
    Alan John Varghese, Shanqing Liu, Paula Chen, Yaochen Zhu, Jerome Darbon, George Em Karniadakis
    Arxiv

  2. [p2] Algorithms and Differential Game Representations for Exploring Nonconvex Pareto Fronts in High Dimensions
    Shanqing Liu, Paula Chen, Youngkyu Lee, Jerome Darbon
    Arxiv

  3. [p3] Adversarial Physics-Informed Machine Learning for Robust Optimal Safe Predefined-Time Stabilization: A Game-Theoretic Approach
    Nick-Marios T Kokolakis, Shanqing Liu, Jerome Darbon, Rahul Mangharam, George Em Karniadakis
    Arxiv

  4. [p4] A Neural-Operator Preconditioned Newton Method for Accelerated Nonlinear Solvers
    Youngkyu Lee, Shanqing Liu, Jerome Darbon, George Em Karniadakis
    Arxiv

  5. [p5] Automatic Discovery of Optimal Meta-solvers via Multi-objective Optimization
    Youngkyu Lee, Shanqing Liu, Jerome Darbon, George Em Karniadakis
    Arxiv

  6. [p6] Convergence and Error Estimates of A Semi-Lagrangian scheme for the Minimum Time Problem
    Marianne Akian, Shanqing Liu
    Arxiv

Journal

  1. [j1] Automatic Selection of the Best Neural Architecture for Time Series Forecasting via Multi-objective Optimization and Pareto Optimality Conditions
    Qianying Cao, Shanqing Liu, Alan John Varghese, Jerome Darbon, Michael Triantafyllou, George Em Karniadakis
    To appear, Nature Communications
    Arxiv

  2. [j2] Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs
    Youngkyu Lee, Shanqing Liu, Jerome Darbon, George Em Karniadakis
    To appear, Journal of Computational Physics
    Arxiv

  3. [j3] Fast Meta-solvers for 3D Complex-shape Scatterers Using Neural Operators Trained on a Non-scattering Problem
    Youngkyu Lee, Shanqing Liu, Zongren Zou, Adar Kahana, Eli Turkel, Rishikesh Ranade, Jay Pathak, George Em Karniadakis
    Computer Methods in Applied Mechanics and Engineering
    DOI Arxiv

  4. [j4] A time-dependent Symplectic Network for Non-convex Path Planning Problems with Linear and Nonlinear Dynamics
    Zhen Zhang, Chenye Wang, Shanqing Liu, Jerome Darbon, George Karniadakis
    SIAM Journal on Scientific Computing
    DOI Arxiv

  5. [j5] Safe Physics-Informed Machine Learning for Optimal Predefined-Time Stabilization: A Lyapunov-based Approach
    Nick-Marios T. Kokolakis, Zhen Zhang, Shanqing Liu, Kyriakos G. Vamvoudakis, Jerome Darbon, George Karniadakis
    IEEE Transactions on Neural Networks and Learning Systems
    DOI

  6. [j6] A Multilevel Fast Marching Method for the Minimum Time Problem
    Marianne Akian, Stéphane Gaubert, and Shanqing Liu
    SIAM Journal on Control and Optimization
    DOI Arxiv

Proceedings of Conference

  1. [c1] An Adaptive Multi-level Max-plus Method for Deterministic Optimal Control Problems
    Marianne Akian, Stéphane Gaubert, and Shanqing Liu
    IFAC-PapersOnLine
    DOI Arxiv

  2. [c2] A Multilevel Fast-marching Method
    Marianne Akian, Stéphane Gaubert, and Shanqing Liu
    MTNS 2022-25th International Symposium on Mathematical Theory of Networks and Systems
    HAL

  3. [c3] Pinns in Pde Constrained Optimal Control Problems: Direct vs Indirect Methods
    Zhen Zhang, Shanqing Liu, Alessandro Alla, Jerome Darbon, George Em Karniadakis
    submitted
    Arxiv

  4. [c4] Tropical Low-rank Approximation and Application to Optimal Control of N-body systems
    Marianne Akian, Stephane Gaubert, Shanqing Liu, Yang Qi
    submitted
    Arxiv

Ph.D. thesis

  1. Highway hierarchies for Hamilton-Jacobi-Bellman (HJB) PDEs
    Supervised by Marianne Akian, co-director of thesis, and Stéphane Gaubert, co-director of thesis
    CMAP, École Polytechnique
    THESES.FR HAL

Teaching

  1. MAA103-Discrete Mathematics
    École Polytechnique, Palaiseau, France, 2020, 2021, 2022
    Bachelor course

  2. MAA107-Mathematical Modeling
    École Polytechnique, Palaiseau, France, 2021
    Bachelor course

Services

Organization

Journal Reviewers


Powered by Jekyll and Minimal Light theme.