Concepedia

Partial Differential Equation Models

Partial Differential Equation Models is a mathematical modeling framework that employs partial differential equations to describe the spatiotemporal dynamics of physiological systems, distinguishing it from ordinary differential equation models by explicitly accounting for variations in both space and time.

1.9K

Publications

114.4K

Citations

3.7K

Authors

1.5K

Institutions

Publications per year

2017–2026

547

Variants

Pde Models

Parents

Children

Publications

1.9K

DGM: A deep learning algorithm for solving partial differential equations

Justin Sirignano, Konstantinos Spiliopoulos · Journal of Computational Physics · 2018 · 2.1K citations · Full text

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An energy approach to the solution of partial differential equations in computational mechanics via machine learning: Concepts, implementation and applications

Esteban Samaniego, Cosmin Anitescu, Somdatta Goswami et al. · Computer Methods in Applied Mechanics and Engineering · 2020 · 1.9K citations · Full text

, , +17

The partial differential equation u<sub>t</sub> + uu<sub>x</sub> = μ<sub>xx</sub>

Eberhard Hopf · Communications on Pure and Applied Mathematics · 1950 · 1.9K citations

, , +7

Data-driven discovery of partial differential equations

Samuel Rudy, Steven L. Brunton, Joshua L. Proctor et al. · Science Advances · 2017 · 1.5K citations · Full text

, , +16

Hidden physics models: Machine learning of nonlinear partial differential equations

Maziar Raissi, George Em Karniadakis · Journal of Computational Physics · 2017 · 1.4K citations · Full text

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1–5 of 1.9K

Authors

3.7K

  1. AW
    Abdul‐Majid Wazwaz

    Saint Xavier University, United States

    13 publications · 945 citations

    13

    h-index

  2. DB
    Dumitru Bǎleanu

    Çankaya University, Türkiye

    10 publications · 420 citations

    10

    h-index

  3. CM
    Chaudry Masood Khalique

    North-West University, South Africa

    9 publications · 421 citations

    9

    h-index

  4. DL
    D. Lesnic

    University of Leeds, United Kingdom

    9 publications · 231 citations

    9

    h-index

  5. GE
    George Em Karniadakis

    Brown University, United States

    8 publications · 5.1K citations

    8

    h-index

1–5 of 3.7K

Institutions

1.5K

  1. Centre National de la Recherche Scientifique

    Paris, France

    27 h-index

    99 publications

    3.9K citations

  2. Massachusetts Institute of Technology

    Cambridge, United States

    14 h-index

    24 publications

    1.7K citations

  3. Brown University

    Providence, United States

    14 h-index

    27 publications

    9.4K citations

  4. Cornell University

    Ithaca, United States

    14 h-index

    25 publications

    2.3K citations

  5. Peking University

    Beijing, China

    14 h-index

    24 publications

    3.3K citations

  6. Sapienza University of Rome

    Rome, Italy

    13 h-index

    27 publications

    1.4K citations

  7. Saint Xavier University

    Chicago, United States

    13 h-index

    13 publications

    945 citations

  8. University of Leeds

    Leeds, United Kingdom

    13 h-index

    25 publications

    681 citations

1–8 of 1.5K

Venues

  1. Journal of Computational Physics

    68 publications · 10K citations

    37

    h-index

  2. Applied Mathematics and Computation

    56 publications · 3.7K citations

    33

    h-index

  3. 26

    h-index

  4. Physics Letters A

    31 publications · 2.3K citations

    24

    h-index

  5. Communications in Partial Differential Equations

    29 publications · 1.7K citations

    22

    h-index

1–5