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 】

• Local profiles of self-similar solutions of the planar stationary Navier--Stokes equations

  M Li, L Peng, P Zhang, X Zhang

  arXiv preprint arXiv:2602.03341  2026

• Hyper-Differential Operator-Based Graph Fractional Fourier Transform: Novel Approaches and Applications

  JY Chen, BZ Li, L Peng

  IEEE Transactions on Signal and Information Processing over Networks  2026

  • Access to Document (DOI)

• -invariant integrable systems from factorisation of linear differential and difference operators

  F Nijhoff, L Peng, C Zhang, D Zhang

  arXiv preprint arXiv:2603.18386  2026

• Stochastic multisymplectic PDEs and their structure-preserving numerical methods

  Ruiao Hu, Linyu Peng

  Studies in Applied Mathematics 155 ( 3 )  2025.09

  ISSN  00222526

  　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)

• Operator-based graph linear canonical transform

  Jian-Yi Chen, Bing-Zhao Li, Linyu Peng

  Journal of the Franklin Institute 362 ( 12 )  2025.08

  ISSN  00160032

  　View Summary

  This paper proposes a novel graph linear canonical transform framework based on hyper-differential operators, referred to as OGLCT. First, the relationship between the graph fractional Fourier transform (GFrFT) and the graph Fourier transform (GFT) is analyzed, and hyper-differential operators associated with the GFT matrix are derived through solutions to the Sylvester equation. Using these operators, the GFrFT, graph scaling, and graph chirp modulation are defined, culminating in the formal definition of the OGLCT and its fundamental properties. Next, the implementation of the OGLCT is discussed, and parameter optimization techniques are explored. Finally, the application of the OGLCT for feature extraction in image processing is explored, and its effectiveness in image classification tasks is investigated. By adjusting the parameters of the OGLCT, it is demonstrated that flexible tuning significantly enhances model performance, enabling more effective and versatile applications.

  • Access to Document (DOI)

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

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

• Multisymplectic geometry and geometric numerical integrator for variational problems

  Peng, Linyu

  科学研究費補助金研究成果報告書 2023

• 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 】

• $\mathrm{PGL}(3)$-invariant integrable systems from factorisation of linear differential and difference operators

  Frank Nijhoff, Linyu Peng, Cheng Zhang, Da-jun Zhang

   2026.03

  　View Summary

  In this paper, we present a unified approach to constructing continuous and discrete $\mathrm{PGL}(3)$-invariant integrable systems, formulated in terms of the common dependent variables $z_1,z_2$, from linear spectral problems and their factorisation. Starting from third-order spectral problems, we first provide explicit forms of the differential and difference invariants, generalising the Schwarzian derivative and cross-ratio to the rank-$3$ setting. The factorisation induces dualities among linear spectral problems, underlying the exact discretisation and multi-dimensional consistency of the associated Boussinesq systems. Then, we derive both continuous and discrete $\mathrm{PGL}(3)$-invariant Boussinesq systems, representing natural rank-$3$ generalisations of the Schwarzian KdV and cross-ratio equations. A geometric lifting-decoupling mechanism is developed to explain the reduction of these systems to the $\mathrm{PGL}(2)$-invariant Boussinesq equations. Finally, we derive a ${\mathrm{PGL } }(3)$-invariant system of generating PDEs together with its Lagrangian structure, in which the lattice parameters serve as independent variables, providing the generating PDE system for the Boussinesq hierarchy.

• Analysis of molecular dynamics simulation data via statistical distances between covariance matrices

  Yusuke Ono, Takumi Sato, Kenji Yasuoka, Linyu Peng

  arXiv preprint arXiv:2603.17318  2026.03

  　View Summary

  Molecular dynamics (MD) simulations are powerful tools for elucidating the macroscopic physical properties of materials from microscopic atomic behaviors. However, the massive, high-dimensional datasets generated by MD simulations pose a significant challenge for analysis, necessitating efficient dimensionality reduction and feature extraction techniques. While existing methods such as principal component analysis and unsupervised learning have been utilized, issues regarding data efficiency and computational cost remain. In this study, we propose a statistical analysis framework focusing on the analysis of the particle data distributions through their covariance matrices, corresponding to the second-order moments of MD trajectory data. Discrepancies between system states are quantified using statistical distances between these covariance matrices. By applying dimensionality reduction to the resulting distance matrix, we extract lower-dimensional features that characterize the systems' dynamics. We validate the proposed method using Lennard-Jones (LJ) particle systems under different temperature conditions, as well as separate bulk systems of ice and liquid water. The results of LJ particles demonstrate an approximately linear correlation between the first principal component obtained through dimensionality reduction of the distance matrix and the diffusion coefficient. This suggests that global physical properties can be effectively inferred from local statistical information, such as covariance matrices, offering a data-efficient alternative for analyzing complex molecular systems. Furthermore, in the case of separate bulk systems of ice and liquid water, the method successfully distinguishes between the two phases, highlighting its potential for characterizing phase transitions and structural differences in molecular systems.

• Euler–Poincaré reduction and the Kelvin–Noether theorem for discrete mechanical systems with advected parameters and additional dynamics

  Physica Scripta  2026.03

  • Access to Document (DOI)

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

  Journal of Mathematical Physics  2025.09

  • Access to Document (DOI)

• Modulated Diffusion: Accelerating Generative Modeling with Modulated Quantization

  Weizhi Gao, Zhichao Hou, Junqi Yin, Feiyi Wang, Linyu Peng, Xiaorui Liu

  arXiv preprint arXiv:2506.22463 (arXiv)   2025.06

  　View Summary

  Diffusion models have emerged as powerful generative models, but their high
  computation cost in iterative sampling remains a significant bottleneck. In
  this work, we present an in-depth and insightful study of state-of-the-art
  acceleration techniques for diffusion models, including caching and
  quantization, revealing their limitations in computation error and generation
  quality. To break these limits, this work introduces Modulated Diffusion
  (MoDiff), an innovative, rigorous, and principled framework that accelerates
  generative modeling through modulated quantization and error compensation.
  MoDiff not only inherents the advantages of existing caching and quantization
  methods but also serves as a general framework to accelerate all diffusion
  models. The advantages of MoDiff are supported by solid theoretical insight and
  analysis. In addition, extensive experiments on CIFAR-10 and LSUN demonstrate
  that MoDiff significant reduces activation quantization from 8 bits to 3 bits
  without performance degradation in post-training quantization (PTQ). Our code
  implementation is available at https://github.com/WeizhiGao/MoDiff.

  • Access to Document (DOI)

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Presentations 【 Display / hide 】

Presentations 【 Display / hide 】

• Discrete Lagrangian multiforms on the difference variational bicomplex

  Linyu Peng

  [International presentation]  BIRS Workshop Lagrangian Multiform Theory and Pluri-Lagrangian Systems, 

  2023.10

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

  Linyu Peng

  [Domestic presentation]  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

  [International presentation]  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

  [International presentation]  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

  [International presentation]  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 】

• INDEPENDENT STUDIES IN MECHANICAL ENGINEERING

  2026

• MECHANICAL ENGINEERING SEMINAR 2

  2026

• MATHEMATICAL SCIENCES PRACTICAL RESEARCH ACTIVITY E

  2026

• DOCTORAL RESEARCH ON ENGINEERING AND DESIGN

  2026

• MATHEMATICAL SCIENCES PRACTICAL RESEARCH ACTIVITY B

  2026

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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