Research

Preprints

Moments, time-inversion and source identification for the heat equation.

K. Liu and E. Zuazua, 2025.

A potential game perspective in Federated Learning.

K. Liu, Z. Wang, and E. Zuazua, 2024.

Universal approximation of dynamical systems by semi-autonomous Neural ODEs and applications.

Z. Li, K. Liu, L. Liverani, and E. Zuazua, 2024.

Mean field optimization problems: stability results and Lagrangian discretization.

K. Liu and L. Pfeiffer, 2023.

Journal articles

Representation and regression problems in Neural Networks: relaxation, generalization, and numerics.

K. Liu and E. Zuazua.

In: Mathematical Models and Methods in Applied Sciences (M3AS), 2025. [doi] [arXiv]

A mesh-independent method for second-order potential mean field games.

K. Liu and L. Pfeiffer.

In: IMA Journal of Numerical Analysis, 2024. [doi] [arXiv]

Large-scale nonconvex optimization: randomization, gap estimation, and numerical resolution.

J.F. Bonnans, K. Liu, N. Oudjane, L. Pfeiffer, and C. Wan.

In: SIAM Journal on Optimization, 2023. [doi] [arXiv]

Error estimates of a theta-scheme for second-order mean field games.

J.F. Bonnans, K. Liu, and L. Pfeiffer.

In: ESAIM: Mathematical Modeling and Numerical Analysis (M2AN), 2023. [doi] [arXiv]

Approximate Nash equilibria in large nonconvex aggregative games.

K. Liu, N. Oudjane, and C. Wan.

In: Mathematics of Operations Research, 2022. [doi] [arXiv]

Conference proceedings

Decomposed resolution of finite-state aggregative optimal control problems.

K. Liu, N. Oudjane, and L. Pfeiffer.

In: SIAM CT23, 2023. [proceeding]

Slides

Neural networks

Universal approximation and convexified training in neural networks

Inverse problem

Moments and initial source identification of heat equation

Game theory

Optimization and optimal control

Presentations (full list)

2025.09, ENUMATH2025, A Theta-scheme for second-order MFG and its mesh-independent resolution, Universität Heidelberg, German.
2025.07-08, academic visits in China, A representer theorem and its applications in neural networks and inverse problems, Jilin University, Shanghai Jiao Tong University, Jiangnan University, and Chinese Academy of Science, China.
2025.07, VC2025 on Optimal Control and Dynamic Games, Moments and initial source identification of heat equation, TU Wien, Austria.
2025.07, DeustoCCM Seminar, Universal approximation and convexified training in neural networks, University of Deusto, Bilbao, Spain.
2025.06, MASPIN Days, Approximation of dynamical systems by semi-autonomous neural ODEs, ENSMM, Besançon, France.
2025.06, Recent progress in Hamilton-Jacobi equations and related topics & Overseas alumni academic forum, Numerical analysis and methods for potential mean-field games; Universal approximation and convexified training in neural networks, Nanjing University, China.
2025.05, AI + 创想会, 在技术浪潮中学习前行 —— AI发展对创业的启示, 中法人工智能协会, Paris, France.
2025.04, DOR de l'IMB avec CNRS, Approximation et optimisation des réseaux de neurones, Institut de Mathématiques de Bourgogne, France.
2025.01, SPOC Day, Universal approximation of dynamical systems by SA-NODE, Institut de Mathématiques de Bourgogne, France.
2025.01, Prob&Stat seminar, Representation and regression problems in neural networks, Laboratoire de mathématiques de Besançon, France.
2024.11, PGMO Days, Universal approximation of dynamical systems by Semi-Autonomous Neural ODEs, EDF-Lab Saclay, France.
2024.10, SPOC seminar, Representation and regression problems in neural networks, Institut de Mathématiques de Bourgogne, France.
2024.10, Conference ANR COSS, Decomposed resolution of multi-agent aggregative optimal control problems, Université de Rennes, France.
2024.08, X Partial differential equations, optimal design and numerics workshop, Representation and regression problems in neural networks; Distributed resolution of high-dimensional aggregative optimal control problems, Benasque Science Center, Spain.
2024.03, SPOC seminar, Non-convex aggregative and mean-field optimization problems, Institut de Mathématiques de Bourgogne, France.
2024.02, DCN-AvH seminar, Aggregative optimization problems and their mean-field relaxation, FAU Erlangen-Nürnberg, German.
2023.10, Ph.D. Defense, Numerical analysis and methods for mean-field type optimization problems, video link, Ecole Polytechnique, France.
2023.07, SIAM CT23, Decomposed resolution of finite-state aggregative optimal control problems, Philadelphia, U.S.A.
2023.06, FiME Ph.D. seminar, Error estimates of a theta-scheme of second-order mean field games (blackboard), Institut Henri-Poincaré, France.
2023.05, Congrès SMAI 2023, Error estimates of a theta-scheme of second-order mean field games, Le Gosier, Guadeloupe.
2023.02, Paris Saclay Ph.D. seminar, Mean field games and a theta-scheme, Orsay, France.
2022.11, PGMO Days, Error estimates of a Theta-scheme of second-order mean field games, EDF-Lab Saclay, France.
2022.10, Hankou Road seminar, Mean field games: an introduction to the theory and numerical methods, by Zoom, Nanjing University, China.
2022.10, FiME seminar, Large-scale nonconvex optimization, Institut Henri-Poincaré, France.
2022.09, KouShare, Mean field games: an introduction, by Zoom, Bilibili link, China.
2022.06, SMAI-MODE, Large scale nonconvex optimization (poster), Limoges University, France.
2022.05, FGP22, Nonconvex optimization and randomization, Faculty of Economics of the University of Porto, Portugal.
2021.12, PGMO Days, Large nonconvex aggregative games, EDF-Lab Saclay, France.

Thesis

K. Liu, Numerical analysis and methods for mean-field type optimization problems. Ph.D. Thesis at École Polytechnique, 2023. [HAL]
K. Liu, Data-driven Methods for Uncertainty Quantification Analysis. Master 1 Thesis at TotalEnergies, 2019.

Referee activities

ACC (2025)*1, COAM*1, DCDS-B*1, JDE*1, JMPA*1, JOTA*2, NEUNET*2.

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