KEIO RESEARCHERS INFORMATION SYSTEM

Career 【 Display / hide 】

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

• 2020.04

  -

  2023.03

  Keio University, Assistant Professor

• 2023.04

  -

  Present

  Keio University , Associate Professor

Academic Background 【 Display / hide 】

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 】

Academic Degrees 【 Display / hide 】

• PhD, University of Surrey, Coursework, 2013.09

Research Areas 【 Display / hide 】

Research Areas 【 Display / hide 】

• Natural Science / Basic mathematics (Applied Mathematics)

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

Research Keywords 【 Display / hide 】

Research Keywords 【 Display / hide 】

• Symmetries and conservation laws

• Geometric mechanics

• Geometric integration

• Information geometry

Books 【 Display / hide 】

Books 【 Display / hide 】

• Mathematical Foundations of Information Geometry

  H. Sun, L. Peng, Y. Cheng, D. Li, L. Jiu,, Science Press, Beijing, 2025.03

• 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, 2011

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

Papers 【 Display / hide 】

Papers 【 Display / hide 】

• The Effect of Accuracy of Initial Velocity Discretisations on Discrete Energy in Variational Integration

  M Gunji, Y Ono, L Peng

  Proceedings of the IUTAM Symposium on Nonlinear Dynamics for Design of … (Springer Cham)     88 - 98 2025.01

• Euler--Poincar\'e reduction and the Kelvin--Noether theorem for discrete mechanical systems with advected parameters and additional dynamics

  Y Ono, S Fiori, L Peng

  arXiv preprint arXiv:2501.12940  2025

• Neural bidomain model for multidimensional ephaptic coupling of neural spike propagation along myelinated fiber bundles with the nodes of Ranvier

  S Chun, L Peng, HJ Park

  bioRxiv  2024.12

  • Access to Document (DOI)

• 半離散方程式の対称性と群不変解

  彭林玉， 富田繁， 郡司士

  Jxiv, JST プレプリントサーバ  2024.11

  　View Summary

  半離散方程式（微分差分方程式ともいう）においては，連続独立変数と離散独立変数が非可換のため，対称性とならない非内在（non-intrinsic）（または不規則（irregular））な変換が生じるという問題があった．本論文では，この問題の解決方法を論じるとともに，半離散方程式における対称性理論について紹介する．具体例として，戸田型，ヴォルテラ型，5 点の伊藤・成田・ボゴヤヴレンスキー方程式などのリー点対称性（Lie point symmetry）を求め，群不変解（group-invariant solution）を導出する．

  • Access to Document (DOI)

• Discrete Dirac structures and discrete Lagrange--Dirac dynamical systems in mechanics

  Linyu Peng, Hiroaki Yoshimura

  arXiv preprint arXiv:2411.09530  2024.11

  　View Summary

  In this paper, we propose the concept of $(\pm)$-discrete Dirac structures
  over a manifold, where we define $(\pm)$-discrete two-forms on the manifold and
  incorporate discrete constraints using $(\pm)$-finite difference maps.
  Specifically, we develop $(\pm)$-discrete induced Dirac structures as discrete
  analogues of the induced Dirac structure on the cotangent bundle over a
  configuration manifold, as described by Yoshimura and Marsden (2006). We
  demonstrate that $(\pm)$-discrete Lagrange--Dirac systems can be naturally
  formulated in conjunction with the $(\pm)$-induced Dirac structure on the
  cotangent bundle. Furthermore, we show that the resulting equations of motion
  are equivalent to the $(\pm)$-discrete Lagrange--d'Alembert equations proposed
  in Cort\'es and Mart\'inez (2001) and McLachlan and Perlmutter (2006). We also
  clarify the variational structures of the discrete Lagrange--Dirac dynamical
  systems within the framework of the $(\pm)$-discrete
  Lagrange--d'Alembert--Pontryagin principle. Finally, we validate the proposed
  discrete Lagrange--Dirac systems with some illustrative examples of
  nonholonomic systems through numerical tests.

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

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

• Symmetry methods for continuous and discrete systems

  Peng, Linyu

  福澤諭吉記念慶應義塾学事振興基金事業報告集 (福澤基金運営委員会)  2023

Reviews, Commentaries, etc. 【 Display / hide 】

Reviews, Commentaries, etc. 【 Display / hide 】

• Stochastic multisymplectic PDEs and their structure-preserving numerical methods

  Ruiao Hu, Linyu Peng

  arXiv preprint arXiv:2501.16913 (arXiv)   2025.01

  　View Summary

  We construct stochastic multisymplectic systems by considering a stochastic
  extension to the variational formulation of multisymplectic partial
  differential equations proposed in [Hydon, {\it Proc. R. Soc. A}, 461,
  1627--1637, 2005]. The stochastic variational principle implies the existence
  of stochastic $1$-form and $2$-form conservation laws, as well as conservation
  laws arising from continuous variational symmetries via a stochastic Noether's
  theorem. These results are the stochastic analogues of those found in
  deterministic variational principles. Furthermore, we develop stochastic
  structure-preserving collocation methods for this class of stochastic
  multisymplectic systems. These integrators possess a discrete analogue of the
  stochastic $2$-form conservation law and, in the case of linear systems, also
  guarantee discrete momentum conservation. The effectiveness of the proposed
  methods is demonstrated through their application to stochastic nonlinear
  Schr\"odinger equations featuring either stochastic transport or stochastic
  dispersion.

  • Access to Document (DOI)

Presentations 【 Display / hide 】

Presentations 【 Display / hide 】

• Discrete Lagrangian multiforms on the difference variational bicomplex

  Linyu Peng

  BIRS Workshop Lagrangian Multiform Theory and Pluri-Lagrangian Systems, 

  2023.10

• 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, 

  2023.09

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

  Y. Ono, L. Peng

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

  2023.08

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

  H. Yoshimura, L. Peng

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

  2023.08

• 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), 

  2023.07

  -

  2023.08

  , 

  Poster presentation

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

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

• Symmetry Methods for Discrete Equations and Their Applications

  2024.04

  -

  2028.03

  Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Principal investigator

  　View Summary

  Symmetries have proven to be of great importance in various fields, owing to the versatile applications in elucidating solution properties to physical models. Many scholars made substantial contributions to the study of symmetry methods for discrete equations, giving rise to a plethora of subsequent research and applications. Despite these advancements, a multitude of unresolved questions continued to challenge the field. The primary objective of the current project is to tackle some of the unresolved questions concerning the symmetries of discrete equations and to explore their applications.

• Multisymplectic Geometry and Geometric Numerical Integrator for Variational Problems

  2020.04

  -

  2024.03

  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 】

Courses Taught 【 Display / hide 】

• PROJECT LABORATORY IN MECHANICAL ENGINEERING

  2025

• NONLINEAR DYNAMICS

  2025

• LIBERAL ARTS AND SCIENCES SEMINAR (GIC) 1

  2025

• LAGRANGIAN AND HAMILTONIAN DYNAMICS

  2025

• INDEPENDENT STUDY ON SCIENCE FOR OPEN AND ENVIRONMENTAL SYSTEMS

  2025

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Memberships in Academic Societies 【 Display / hide 】

Memberships in Academic Societies 【 Display / hide 】

• Institute of Electrical and Electronics Engineers, 

  2021.07

  -

  Present

• The Japan Society of Mechanical Engineers, 

  2021.01

  -

  Present

• The Mathematical Society of Japan, 

  2018.10

  -

  Present

• The Japan Society for Industrial and Applied Mathematics, 

  2018.06

  -

  Present