Peng, Linyu

写真a

Affiliation

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

Position

Senior Assistant Professor (Non-tenured)/Assistant Professor (Non-tenured)

External Links

Career 【 Display / hide

  • 2013.10
    -
    2015.03

    Waseda University, Junior Researcher

  • 2015.04
    -
    2017.03

    Waseda University , Assistant Professor

  • 2017.04
    -
    2020.03

    Waseda University, Assistant Professor

Academic Background 【 Display / hide

  • 2004.09
    -
    2008.06

    Beijing Institute of Technology

    University, Graduated

  • 2008.09
    -
    2010.07

    Beijing Institute of Technology

    Graduate School, Completed, Master's course

  • 2010.10
    -
    2013.07

    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

  • A stochastic Hamiltonian formulation applied to dissipative particle dynamics

    L Peng, N Arai, K Yasuoka

    arXiv preprint arXiv:2203.12183 (Elsevier {BV})  426   127126 - 127126 2022

    ISSN  00963003

     View Summary

    In this paper, a stochastic Hamiltonian formulation (SHF) is proposed and applied to dissipative particle dynamics (DPD) simulations. As an extension of Hamiltonian dynamics to stochastic dissipative systems, the SHF provides necessary foundations and great convenience for constructing efficient numerical integrators. As a first attempt, we develop the Störmer–Verlet type of schemes based on the SHF, which are structure-preserving for deterministic Hamiltonian systems without external forces, the dissipative forces in DPD. Long-time behaviour of the schemes is shown numerically by studying the damped Kubo oscillator. In particular, the proposed schemes include the conventional Groot–Warren's modified velocity-Verlet method and a modified version of Gibson–Chen–Chynoweth as special cases. The schemes are applied to DPD simulations and analysed numerically.

  • Unsupervised Learning Discriminative MIG Detectors in Nonhomogeneous Clutter

    Xiaoqiang Hua, Yusuke Ono, Linyu Peng, Yuting Xu

    IEEE Transactions on Communications (Institute of Electrical and Electronics Engineers ({IEEE}))     1 - 1 2022

    ISSN  00906778

     View Summary

    Principal component analysis (PCA) is a common used pattern analysis method that maps high-dimensional data into a lower-dimensional space maximizing the data variance, that results in the promotion of separability of data. Inspired by the principle of PCA, a novel type of learning discriminative matrix information geometry (MIG) detectors in the unsupervised scenario are developed, and applied to signal detection in nonhomogeneous environments. Hermitian positive-definite (HPD) matrices can be used to model the sample data, while the clutter covariance matrix is estimated by the geometric mean of a set of secondary HPD matrices. We define a projection that maps the HPD matrices in a high-dimensional manifold to a low-dimensional and more discriminative one to increase the degree of separation of HPD matrices by maximizing the data variance. Learning a mapping can be formulated as a two-step mini-max optimization problem in Riemannian manifolds, which can be solved by the Riemannian gradient descent algorithm. Three discriminative MIG detectors are illustrated with respect to different geometric measures, i.e., the Log-Euclidean metric, the Jensen–Bregman LogDet divergence and the symmetrized Kullback–Leibler divergence. Simulation results show that performance improvements of the novel MIG detectors can be achieved compared with the conventional detectors and their state-of-the-art counterparts within nonhomogeneous environments.

  • Towards a median signal detector through the total Bregman divergence and its robustness analysis

    Y Ono, L Peng

    Signal Processing, 108728 (Elsevier {BV})  201   108728 2022

    ISSN  01651684

     View Summary

    A novel family of geometric signal detectors are proposed through medians of the total Bregman divergence (TBD), which are shown advantageous over the conventional methods and their mean counterparts. By interpreting the observation data as Hermitian positive-definite matrices, their mean or median play an essential role in signal detection. As is difficult to be solved analytically, we propose numerical solutions through Riemannian gradient descent algorithms or fixed-point algorithms. Beside detection performance, robustness of a detector to outliers is also of vital importance, which can often be analyzed via the influence functions. Introducing an orthogonal basis for Hermitian matrices, we are able to compute the corresponding influence functions analytically and exactly by solving a linear system, which is transformed from the governing matrix equation. Numerical simulations show that the TBD medians are more robust than their mean counterparts.

  • Transformations, symmetries and Noether theorems for differential-difference equations

    L Peng, PE Hydon

    arXiv preprint arXiv:2112.06030 (The Royal Society)  478 ( 2259 )  2021.12

    Research paper (scientific journal), Joint Work, Accepted,  ISSN  13645021

     View Summary

    The first part of this paper develops a geometric setting for
    differential-difference equations that resolves an open question about the
    extent to which continuous symmetries can depend on discrete independent
    variables. For general mappings, differentiation and differencing fail to
    commute. We prove that there is no such failure for structure-preserving
    mappings, and identify a class of equations that allow greater freedom than is
    typical.
    For variational symmetries, the above results lead to a simple proof of the
    differential-difference version of Noether's Theorem. We state and prove the
    differential-difference version of Noether's Second Theorem, together with a
    Noether-type theorem that spans the gap between the analogues of Noether's two
    theorems. These results are applied to various equations from physics.

  • MIG Median Detectors with Manifold Filter

    Xiaoqiang Hua, Linyu Peng

    Signal Processing  2021.05

    Research paper (scientific journal), Joint Work, Accepted

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Reviews, Commentaries, etc. 【 Display / hide

Presentations 【 Display / hide

  • Variational systems on the variational bicomplex

    PENG Linyu

    Seminar at INI, Cambridge University, 

    2019.09

    Oral presentation (general)

  • A general prolongation formulation for symmetries of differential-difference equations

    PENG Linyu

    China-Japan Joint Workshop on Integrable Systems 2019, 

    2019.08

    Oral presentation (general)

  • Symmetries of semi-discrete variational problems and Noether's theorems

    PENG Linyu

    Symmetry and Singularity of Geometric Structures and Differential Equations, 

    2018.12

    Oral presentation (general)

  • The discrete Lagrange-d’Alembert principle for physical systems with constraints

    PENG Linyu, YOSHIMURA Hiroaki

    The 5th International Conference on Dynamics, Vibration and Control, 

    2018.07

    Oral presentation (general)

  • Symmetries and Conservation Laws of Semi-Discrete Equations

    PENG Linyu

    The 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications, 

    2018.07

    Oral presentation (general)

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

  • Multisymplectic Geometry and Geometric Numerical Integrator for Variational Problems

    2020.04
    -
    Present

    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

    2016.04
    -
    2019.03

    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

  • STABILITY THEORY IN DYNAMICS SYSTEMS

    2022

  • SPECIAL LECTURE IN MECHANICAL ENGINEERING

    2022

  • SPECIAL LECTURE IN MATHEMATICAL SCIENCE 1

    2022

  • PROJECT LABORATORY IN MECHANICAL ENGINEERING

    2022

  • NONLINEAR DYNAMICS

    2022

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Memberships in Academic Societies 【 Display / hide

  • The Mathematical Society of Japan, 

    2018.10
    -
    Present
  • The Japan Society for Industrial and Applied Mathematics, 

    2018.06
    -
    Present