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Topic · Statistical and Nonlinear Physics

Model Reduction and Neural Networks

Model Reduction and Neural Networks is a research topic within Statistical and Nonlinear Physics. Science Explorer counts 25k research works in it since 1950. 21.3% of them reached the world's top 10% most cited for their field and year.

This cluster of papers focuses on the development and application of physics-informed neural networks for scientific computing, particularly in the context of solving partial differential equations, model reduction, fluid dynamics, dynamic mode decomposition, and nonlinear systems. The research explores the integration of deep learning techniques with traditional numerical methods to address complex problems in physics-based modeling and simulation.

  • Deep Learning
  • Partial Differential Equations
  • Model Reduction
  • Fluid Dynamics
  • Dynamic Mode Decomposition
  • Nonlinear Systems
  • Machine Learning
  • Data-Driven Modeling
  • Numerical Computing
  • Inverse Problems
Research works
25k
fractional, since 1950
In the world top 10%
5.3k
per year above
Top-10% rate
21.3%
share of its works in the world top 10%
Growth, 2013–17 → 2018–22
+85%
the tick is no change

Which countries lead Model Reduction and Neural Networks research?

By volume, China and the United States publish the most (1.9k and 1.7k works in 2022–2025).

By volume, 2022–2025

  1. 1 China 1.9k works
  2. 2 United States 1.7k works
  3. 3 Germany 558 works
  4. 4 France 334 works
  5. 5 United Kingdom 304 works
  6. 6 India 285 works
  7. 7 Italy 238 works
  8. 8 Japan 219 works
  9. 9 South Korea 150 works
  10. 10 Canada 148 works

How concentrated that is

The same countries as shares of everything the list above accounts for. A node where two countries do two thirds of the work and one spread evenly across twelve read alike as a ranking and not at all alike here.

China: 32.5%United States: 29.4%Germany: 9.5%France: 5.7%6 others listed: 22.9%32%largest
China1,900 · 32.5%United States1,719 · 29.4%Germany558 · 9.5%France334 · 5.7%6 others listed1,344 · 22.9%

Shares of the rows listed above, not of the whole node.

Which institutions lead Model Reduction and Neural Networks research?

By volume in 2022–2025, Northwestern Polytechnical University publishes the most Model Reduction and Neural Networks research, followed by Imperial College London and Tsinghua University.

By volume, 2022–2025

  1. 1 Northwestern Polytechnical UniversityChina 66 works
  2. 2 Imperial College LondonUnited Kingdom 60 works
  3. 3 Tsinghua UniversityChina 52 works
  4. 4 Xi'an Jiaotong UniversityChina 51 works
  5. 5 Shanghai Jiao Tong UniversityChina 51 works
  6. 6 Beihang UniversityChina 49 works
  7. 7 Harbin Institute of TechnologyChina 45 works
  8. 8 University of MichiganUnited States 44 works
  9. 9 Zhejiang UniversityChina 42 works
  10. 10 Centre National de la Recherche ScientifiqueFrance 41 works

Who are the leading researchers in Model Reduction and Neural Networks?

The most-cited researchers publishing on Model Reduction and Neural Networks include Yoshua Bengio, Stanley Osher and George Em Karniadakis.

  1. 1 Yoshua Bengio Canada 17k citations
  2. 2 Stanley Osher United States 8k citations
  3. 3 George Em Karniadakis United States 6.3k citations

Ranked by citations received across their whole record, among researchers with at least three works on this topic.

Where is Model Reduction and Neural Networks research done?

The largest centres of Model Reduction and Neural Networks research in 2022–2025 are Beijing (China), Shanghai (China), Xi'an (China) and Paris (France). Among places with at least 20 works in it, it is an unusually large share of all research in Magdeburg and Livermore.

Largest cities, 2022–2025

  1. 1 Beijing China 400 works
  2. 2 Shanghai China 178 works
  3. 3 Xi'an China 164 works
  4. 4 Paris France 110 works
  5. 5 Nanjing China 107 works
  6. 6 London United Kingdom 101 works
  7. 7 Tokyo Japan 84 works
  8. 8 Changsha China 83 works
  9. 9 Hangzhou China 77 works
  10. 10 Harbin China 67 works

Where it is the local speciality

  1. MagdeburgDE · 31.7 works15×
  2. LivermoreUS · 24.0 works13×
← less than its size predicts1×more →

Location quotient: how much more of its research is in Model Reduction and Neural Networks than the world average.

See Model Reduction and Neural Networks on the map

Where is the best place to study Model Reduction and Neural Networks?

Among universities, judged by research, Scuola Internazionale Superiore di Studi Avanzati, ETH Zurich and Brown University score highest, combining excellence, specialisation, size, growth and international reach. Research strength is one signal when choosing where to study; it does not measure teaching.

0%25%50%75%mean 36.84%fractional works in this node (log) →share in the world top 10% →Scuola Internazionale Superiore di Studi Avanzati: 20, 39.6%ETH Zurich: 34, 45.9%Brown University: 20, 70.2%California Institute of Technology: 18, 40.4%Imperial College London: 60, 25.7%University of Notre Dame: 21, 34.0%Northwestern Polytechnical University: 66, 35.6%University of Stuttgart: 25, 27.8%King Abdullah University of Science and Technology: 19, 27.7%École Polytechnique Fédérale de Lausanne: 26, 21.5%Brown UniversityETH ZurichCalifornia Institute…Scuola Internazional…
above the meannear itbelow it

One dot per university in the table below. The upper left is the interesting corner: small places doing unusually strong work.

#UniversityScoreTop 10%SpecialisationWorksGrowth
1 Scuola Internazionale Superiore di Studi AvanzatiItaly 71.639.6%65.2×20 +220.9%
2 ETH ZurichSwitzerland 69.545.9%7.0×34 +177.1%
3 Brown UniversityUnited States 66.070.2%7.2×20 +80.3%
4 California Institute of TechnologyUnited States 64.640.4%10.2×18 +146.6%
5 Imperial College LondonUnited Kingdom 64.325.7%9.2×60 +50.2%
6 University of Notre DameUnited States 63.534.0%9.5×21 +302.3%
7 Northwestern Polytechnical UniversityChina 62.235.6%7.9×66 +69.6%
8 University of StuttgartGermany 55.927.8%9.9×25 +71.7%
9 King Abdullah University of Science and TechnologySaudi Arabia 55.727.7%9.5×19 +39.5%
10 École Polytechnique Fédérale de LausanneSwitzerland 54.921.5%8.8×26 +74.0%

Universities only. Score blends excellence (30%), specialisation (25%), size (20%), growth (15%) and international reach (10%), 2015–2022; growth compares 2010–14 with 2015–19.

Is Model Reduction and Neural Networks research growing?

Output in 2018–2022 was 85% higher than in 2013–2017, peaking in 2025. The fastest-growing topics are Model Reduction and Neural Networks.

19801990200020102020
grewheldshrank

The same series as a ribbon — one cell per year, darker for more. The line above answers how much; this answers when.

Which topics inside it are moving

Growth and decline on one axis around a shared zero. Two lists side by side hide the thing that matters: whether the growth dwarfs the decline, or the other way round.