PENG Linyu



Faculty of Science and Technology, Department of Mechanical Engineering (Yagami)


Associate Professor

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Career 【 Display / hide

  • 2013.10

    Waseda University, Junior Researcher

  • 2015.04

    Waseda University , Assistant Professor

  • 2017.04

    Waseda University, Assistant Professor

  • 2020.04

    Keio University, Assistant Professor

  • 2023.04

    Keio University , Associate Professor

Academic Background 【 Display / hide

  • 2004.09

    Beijing Institute of Technology

    University, Graduated

  • 2008.09

    Beijing Institute of Technology

    Graduate School, Completed, Master's course

  • 2010.10

    University of Surrey

    Graduate School, Completed, Doctoral course

Academic Degrees 【 Display / hide

  • PhD, University of Surrey, Coursework, 2013.09


Research Areas 【 Display / hide

  • Natural Science / Basic mathematics (Applied Mathematics)

  • Natural Science / Applied mathematics and statistics (Applied Mathematics)

Research Keywords 【 Display / hide

  • Symmetries and conservation laws

  • Geometric mechanics

  • Geometric integrator

  • Information geometry


Books 【 Display / hide

  • Paving the Way for 5G Through the Convergence of Wireless Systems

    X. Zhang, Y. Cao, L. Peng, J. Li, IGI Global Publisher, 2019

    Scope: Enhancing Mobile Data Offloading With In-Network Caching,  Contact page: 250-270

  • An Elementary Introduction to Information Geometry

    H. Sun, Z. Zhang, L. Peng, X. Duan, Science Press, Beijing, 2016.03

  • Object Recognition

    F. Li, L. Peng, H. Sun, IntechOpen, 2011.04,  Page: 350

    Scope: Fibre Bundle Models and 3D Object Recognition,  Contact page: 317-332

Papers 【 Display / hide

  • Developing a cloud evidence method for dynamic early warning of tunnel construction safety risk in undersea environment

    H Zhou, B Gao, X Zhao, L Peng, S Bai

    Developments in the Built Environment 16, 100225 (Developments in the Built Environment)  16 2023.12

     View Summary

    Traditional methods have limitations in achieving precise predictions of risk occurrence at an exact future time and have difficulties transforming between qualitative and quantitative indicators and handling multi-source heterogeneous risk data. This study quantifies and analyzes the multi-source construction safety risks classified into the categories of man, machine, material, method and environment (4M1E), and presents a cloud evidence method that integrates wavelet de-noising algorithm, cloud model, and Dempster-Shafer (D-S) evidence theory. A real-time risk prediction and warning is provided using this method after the fusion of multi-source uncertain information and the transformation between qualitative and quantitative indicators, enabling the timely detection of potential risks for project managers. This method analyzing “uncertainty” with “certainty” is verified by an undersea tunnel construction project. The result shows that this method is effective in early warning risks two days before their actual occurrence, providing reference significance for risk early warning of the tunnel construction project.

  • The difference variational bicomplex and multisymplectic systems

    Linyu Peng, Peter E. Hydon

    arXiv preprint arXiv:2307.13935  2023.07

     View Summary

    The difference variational bicomplex, which is the natural setting for
    systems of difference equations, is constructed and used to examine the
    geometric and algebraic properties of various systems. Exactness of the
    bicomplex gives a coordinate-free setting for finite difference variational
    problems, Euler--Lagrange equations and Noether's theorem. We also examine the
    connection between the condition for existence of a Hamiltonian and the
    multisymplecticity of systems of partial difference equations. Furthermore, we
    define difference multimomentum maps of multisymplectic systems, which yield
    their conservation laws. To conclude, we demonstrate how multisymplectic
    integrators can be comprehended even on non-uniform meshes through a
    generalized difference variational bicomplex.

  • Some novel physical structures of a (2+1)-dimensional variable-coefficient Korteweg–de Vries system

    Yaqing Liu, Linyu Peng

    Chaos, Solitons and Fractals (Chaos, Solitons and Fractals)  171 2023.06

    Corresponding author, Accepted,  ISSN  09600779

     View Summary

    In this paper, we study the novel nonlinear wave structures of a (2+1)-dimensional variable-coefficient Korteweg–de Vries (KdV) system by its analytic solutions. Its N-soliton solutions are obtained via Hirota's bilinear method, and in particular, the hybrid solutions of lump, breather and line solitons are derived by the long wave limit method. In addition to soliton solutions, similarity reduction, including similarity solutions (also known as group-invariant solutions) and novel non-autonomous rational third-order Painlevé equations, is achieved through symmetry analysis. The analytic results, together with illustrative wave interactions, show interesting physical features, that may shed some light on the study of other variable-coefficient nonlinear systems.

  • Lagrangian Multiform Theory and Pluri-Lagrangian Systems (23w5043)

    F Nijhoff, L Peng, Y Shi, D Zhang


  • LDA-MIG Detectors for Maritime Targets in Nonhomogeneous Sea Clutter

    X Hua, L Peng, W Liu, Y Cheng, H Wang, H Sun, Z Wang

    IEEE Transactions on Geoscience and Remote Sensing (IEEE Transactions on Geoscience and Remote Sensing)  61 2023

    Accepted,  ISSN  01962892

     View Summary

    This article deals with the problem of detecting maritime targets embedded in nonhomogeneous sea clutter, where the limited number of secondary data is available due to the heterogeneity of sea clutter. A class of linear discriminant analysis (LDA)-based matrix information geometry (MIG) detectors is proposed in the supervised scenario. As customary, Hermitian positive-definite (HPD) matrices are used to model the observational sample data, and the clutter covariance matrix of the received dataset is estimated as the geometric mean of the secondary HPD matrices. Given a set of training HPD matrices with class labels, which are elements of a higher dimensional HPD matrix manifold, the LDA manifold projection learns a mapping from the higher dimensional HPD matrix manifold to a lower dimensional one subject to maximum discrimination. In this study, the LDA manifold projection, with the cost function maximizing between-class distance while minimizing within-class distance, is formulated as an optimization problem in the Stiefel manifold. Four robust LDA-MIG detectors corresponding to different geometric measures are proposed. Numerical results based on both simulated radar clutter with interferences and real IPIX radar data show the advantage of the proposed LDA-MIG detectors against their counterparts without using LDA and the state-of-the-art maritime target detection methods in nonhomogeneous sea clutter.

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Papers, etc., Registered in KOARA 【 Display / hide

Presentations 【 Display / hide

  • Discrete Lagrangian multiforms on the difference variational bicomplex

    Linyu Peng

    BIRS Workshop Lagrangian Multiform Theory and Pluri-Lagrangian Systems, 


  • The modified formal variational formulation for general differential equations and applications

    Linyu Peng

    持続的環境エネルギー社会共創研究機構 研究所間交流会, 


  • Applications of Bures-Wasserstein geometry of HPD matrices to signal detection

    Y. Ono, L. Peng

    10th International Congress on Industrial and Applied Mathematics (ICIAM2023), 


  • A discretization of Dirac structures and Lagrange-Dirac dynamical systems

    H. Yoshimura, L. Peng

    10th International Congress on Industrial and Applied Mathematics (ICIAM2023), 


  • The influence of accuracy of initial values on the discrete energy in variational integrator

    M. Gunji, Y. Ono, L. Peng

    IUTAM Symposium on Nonlinear Dynamics for Design of Mechanical Systems across Different Length/Time Scales (IUTAM2023), 


    Poster presentation

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Research Projects of Competitive Funds, etc. 【 Display / hide

  • Multisymplectic Geometry and Geometric Numerical Integrator for Variational Problems


    Keio University, Grants-in-Aid for Scientific Research, Linyu Peng, Grant-in-Aid for Early-Career Scientists, Research grant, Principal investigator

     View Summary

    Geometric integrator is among one of the most efficient numerical methods for differential equations. In this project, we establish a unified and systematical analogue for understanding both continuous and discrete multisymplectic structures of arbitrary order variational differential equations.

  • 複雑な流体現象のモデリング,マルチスケール構造の解明と数理解析


    Waseda University, Grants-in-Aid for Scientific Research, Hiroaki Yoshimura, Grant-in-Aid for Scientific Research (B), Research grant, Coinvestigator(s)

     View Summary

    We have explored mathematical modeling of complex fluid phenomena, mathematical analysis of partial differential equations and stochastic differential equations associated to multi-scale phenomena as well as applications of nonlinear mechanics. For the mathematical modeling, we have studied a Lagrangian variational formulation of nonequilibrium thermodynamics, modeling of cloud cavitation and with experiments, elucidation of LCS (Lagrangian coherent structures) for Rayleigh-Benard convection as well as a stochastic variational formulation of single bubble dynamics. For the mathematical analysis, we have researched on the existence and uniqueness of Navier-Stokes equations for two-phase flows, stochastic KPZ equations and modified KdV equations. Further we have shown some applications of LCS analysis to space mission design.


Courses Taught 【 Display / hide











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Memberships in Academic Societies 【 Display / hide

  • Institute of Electrical and Electronics Engineers, 

  • The Japan Society of Mechanical Engineers, 

  • The Mathematical Society of Japan, 

  • The Japan Society for Industrial and Applied Mathematics,