D-Index & Metrics Best Publications

D-Index & Metrics

Discipline name D-index D-index (Discipline H-index) only includes papers and citation values for an examined discipline in contrast to General H-index which accounts for publications across all disciplines. Citations Publications World Ranking National Ranking
Mathematics D-index 72 Citations 17,775 320 World Ranking 103 National Ranking 59

Research.com Recognitions

Awards & Achievements

2020 - Member of the National Academy of Engineering For research on multiscale mathematical modeling and scientific computation for complex, nonlinear reaction, and transport processes.

2010 - SIAM Fellow For research contributions in chemical engineering, applied mathematics, and the computational sciences.

Overview

What is he best known for?

The fields of study he is best known for:

  • Quantum mechanics
  • Mathematical analysis
  • Statistics

His main research concerns Statistical physics, Mathematical analysis, Bifurcation, Computation and Nonlinear system. Ioannis G. Kevrekidis combines subjects such as Kinetic Monte Carlo, Monte Carlo method, Numerical analysis, Molecular dynamics and Stochastic process with his study of Statistical physics. His Mathematical analysis study incorporates themes from Eigenvalues and eigenvectors and Dissipative system.

His biological study spans a wide range of topics, including Dynamical systems theory, Dimensional reduction and Dynamic mode decomposition. His Bifurcation study combines topics in areas such as Reaction–diffusion system and Pattern formation. His Nonlinear system study combines topics from a wide range of disciplines, such as Artificial neural network, Partial differential equation, Invariant and Signal processing.

His most cited work include:

  • Diffusion maps, spectral clustering and reaction coordinates of dynamical systems (907 citations)
  • Equation-Free, Coarse-Grained Multiscale Computation: Enabling Mocroscopic Simulators to Perform System-Level Analysis (657 citations)
  • A Data-Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition (652 citations)

What are the main themes of his work throughout his whole career to date?

His scientific interests lie mostly in Statistical physics, Nonlinear system, Computation, Bifurcation and Applied mathematics. His Statistical physics research includes themes of Numerical analysis, Kinetic Monte Carlo, Monte Carlo method and Molecular dynamics. Nonlinear system is a primary field of his research addressed under Control theory.

His study on Computation is covered under Algorithm. His research is interdisciplinary, bridging the disciplines of Mathematical analysis and Bifurcation. His biological study deals with issues like Eigenvalues and eigenvectors, which deal with fields such as Dynamic mode decomposition.

He most often published in these fields:

  • Statistical physics (24.96%)
  • Nonlinear system (17.72%)
  • Computation (15.41%)

What were the highlights of his more recent work (between 2016-2021)?

  • Algorithm (10.32%)
  • Nonlinear dimensionality reduction (5.24%)
  • Nonlinear system (17.72%)

In recent papers he was focusing on the following fields of study:

Ioannis G. Kevrekidis mainly focuses on Algorithm, Nonlinear dimensionality reduction, Nonlinear system, Applied mathematics and Diffusion map. Ioannis G. Kevrekidis has included themes like Scale, Linear system, Mathematical optimization and Classical mechanics in his Nonlinear system study. His work investigates the relationship between Scale and topics such as Waves and shallow water that intersect with problems in Computation.

His work carried out in the field of Applied mathematics brings together such families of science as Probability distribution, Dynamical systems theory, Inverse problem, Importance sampling and Artificial neural network. The concepts of his Diffusion map study are interwoven with issues in Transformation and Model predictive control. His Space study integrates concerns from other disciplines, such as Coupling and Statistical physics.

Between 2016 and 2021, his most popular works were:

  • Data-driven model reduction and transfer operator approximation (138 citations)
  • Data-driven model reduction and transfer operator approximation (138 citations)
  • Extended dynamic mode decomposition with dictionary learning: A data-driven adaptive spectral decomposition of the Koopman operator (127 citations)

In his most recent research, the most cited papers focused on:

  • Quantum mechanics
  • Mathematical analysis
  • Statistics

His primary areas of study are Mathematical optimization, Nonlinear system, Algorithm, Dynamical systems theory and Diffusion map. Ioannis G. Kevrekidis has researched Nonlinear system in several fields, including Optimal control, Algorithm design, Parametric family, Function and Optimization problem. His work in Dynamical systems theory covers topics such as Applied mathematics which are related to areas like Eigenfunction, Finite set, Attractor and Invariant measure.

The Diffusion map study combines topics in areas such as Partial differential equation and Spatial reference system. The study of Time evolution is intertwined with the study of Statistical physics in a number of ways. Statistical physics and Patch dynamics are two areas of study in which he engages in interdisciplinary work.

This overview was generated by a machine learning system which analysed the scientist’s body of work. If you have any feedback, you can contact us here.

Best Publications

Diffusion maps, spectral clustering and reaction coordinates of dynamical systems

Boaz Nadler;Stéphane Lafon;Ronald R. Coifman;Ioannis G. Kevrekidis.
Applied and Computational Harmonic Analysis (2006)

907 Citations

Equation-Free, Coarse-Grained Multiscale Computation: Enabling Mocroscopic Simulators to Perform System-Level Analysis

C. William Gear;James M. Hyman;Panagiotis G Kevrekidid;Ioannis G. Kevrekidis.
Communications in Mathematical Sciences (2003)

878 Citations

A Data-Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition

Matthew O. Williams;Ioannis G. Kevrekidis;Clarence W. Rowley.
Journal of Nonlinear Science (2015)

712 Citations

Low‐dimensional models for complex geometry flows: Application to grooved channels and circular cylinders

A. E. Deane;I. G. Kevrekidis;G. E. Karniadakis;S. A. Orszag.
Physics of Fluids (1991)

559 Citations

Diffusion Maps, Spectral Clustering and Eigenfunctions of Fokker-Planck Operators

Boaz Nadler;Stephane Lafon;Ioannis Kevrekidis;Ronald R. Coifman.
neural information processing systems (2005)

525 Citations

Equation-free: The computer-aided analysis of complex multiscale systems

Ioannis G. Kevrekidis;C. William Gear;Gerhard Hummer.
Aiche Journal (2004)

430 Citations

Back in the saddle again: a computer assisted study of the Kuramoto-Sivashinsky equation

Ioannis G. Kevrekidis;Basil Nicolaenko;James C. Scovel.
Siam Journal on Applied Mathematics (1990)

336 Citations

Approximate inertial manifolds for the Kuramoto-Sivashinsky equation: analysis and computations

M. S. Jolly;I. G. Kevrekidis;E. S. Titl.
Physica D: Nonlinear Phenomena (1990)

297 Citations

Inherent noise can facilitate coherence in collective swarm motion

Christian A. Yates;Radek Erban;Carlos Escudero;Iain D. Couzin.
Proceedings of the National Academy of Sciences of the United States of America (2009)

296 Citations

Projective Methods for Stiff Differential Equations: Problems with Gaps in Their Eigenvalue Spectrum

C. W. Gear;Ioannis G. Kevrekidis.
SIAM Journal on Scientific Computing (2002)

294 Citations

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