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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. 9.9% 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%
2.5k
per year above
Top-10% rate
9.9%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
+108%
the tick is no change
Largest producer
China
36% of the 10 largest, 2022-now
Model Reduction and Neural Networks

Which countries lead Model Reduction and Neural Networks research?

By volume, China and the United States publish the most (2.8k and 2.2k works in 2022-now).

By volume, 2022-now

  1. 1 China 2.8k works
  2. 2 United States 2.2k works
  3. 3 Germany 693 works
  4. 4 India 406 works
  5. 5 United Kingdom 400 works
  6. 6 France 393 works
  7. 7 Italy 296 works
  8. 8 Japan 274 works
  9. 9 South Korea 203 works
  10. 10 Canada 185 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: 35.9%United States: 27.8%Germany: 8.8%India: 5.2%6 others listed: 22.3%36%largest
China2,813 · 35.9%United States2,181 · 27.8%Germany693 · 8.8%India406 · 5.2%6 others listed1,751 · 22.3%

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

Which institutions lead Model Reduction and Neural Networks research?

By volume in 2022-now, Centre National de la Recherche Scientifique publishes the most Model Reduction and Neural Networks research, followed by Chinese Academy of Sciences and Northwestern Polytechnical University.

By volume, 2022-now

  1. 1 Centre National de la Recherche ScientifiqueFrance 142 works
  2. 2 Chinese Academy of SciencesChina 97 works
  3. 3 Northwestern Polytechnical UniversityChina 86 works
  4. 4 Tsinghua UniversityChina 73 works
  5. 5 Imperial College LondonUnited Kingdom 72 works
  6. 6 Xi'an Jiaotong UniversityChina 71 works
  7. 7 Shanghai Jiao Tong UniversityChina 70 works
  8. 8 Helmholtz Association of German Research CentresGermany 69 works
  9. 9 Beihang UniversityChina 67 works
  10. 10 Zhejiang UniversityChina 60 works

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

The most-cited researchers publishing on Model Reduction and Neural Networks include Kaiming He, Yoshua Bengio and Geoffrey E. Hinton.

  1. 1 Kaiming He Israel 562k citations
  2. 2 Yoshua Bengio Canada 476k citations
  3. 3 Geoffrey E. Hinton Canada 454k citations
  4. 4 Kostya S. Novoselov United Kingdom 331k citations
  5. 5 Karl John Friston United Kingdom 310k citations
  6. 6 Yann LeCun United States 256k citations
  7. 7 Andrew Zisserman United Kingdom 255k citations
  8. 8 Aviv Regev United States 236k citations
  9. 9 Kai You Wang China 224k citations
  10. 10 Ilya Sutskever Canada 219k citations

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

What are the most cited papers in Model Reduction and Neural Networks?

The most cited paper in Model Reduction and Neural Networks is "Greedy function approximation: A gradient boosting machine." (Jerome H. Friedman, 2001), with 30,593 citations. Next come "Multilayer feedforward networks are universal approximators" (21,792) and "Reducing the Dimensionality of Data with Neural Networks" (21,368).

Most cited papers
#PaperReleasedCitations
1 Greedy function approximation: A gradient boosting machine. Jerome H. Friedman · The Annals of Statistics Oct 2001 30,593
2 Multilayer feedforward networks are universal approximators Kurt Hornik, Maxwell B. Stinchcombe, Halbert White · Neural Networks 1989 21,792
3 Reducing the Dimensionality of Data with Neural Networks Geoffrey E. Hinton, Ruslan Salakhutdinov · Science 27 Jul 2006 21,368
4 Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations Maziar Raissi, Paris Perdikaris, George Em Karniadakis · Journal of Computational Physics Open access 3 Nov 2018 19,776
5 Physics-informed machine learning George Em Karniadakis, Ioannis G. Kevrekidis, Lu Lu et al. · Nature Reviews Physics ReviewOpen access 24 May 2021 8,059
All 100 most cited papers, with filters and sorting

Where is Model Reduction and Neural Networks research done?

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

Largest cities, 2022-now

  1. 1 BeijingChina 548 works
  2. 2 ShanghaiChina 248 works
  3. 3 Xi'anChina 222 works
  4. 4 NanjingChina 152 works
  5. 5 LondonUnited Kingdom 132 works
  6. 6 ParisFrance 129 works
  7. 7 ChangshaChina 112 works
  8. 8 HangzhouChina 109 works
  9. 9 TokyoJapan 107 works
  10. 10 WuhanChina 96 works

Where it is the local speciality

  1. MagdeburgDE · 36.4 works13×
  2. LivermoreUS · 29.1 works12×
  3. Los AlamosUS · 22.2 works8.8×
← 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, Brown University, Hong Kong Polytechnic University and ETH Zurich 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%20%40%mean 20.56%fractional works in this field (log) →share of work in the world top 10% →Brown UniversityHong Kong Polytechni…ETH ZurichNorthwestern Polytec…
above the meannear itbelow it

One dot per university in the first ten of the table below, at the default weights. The upper left is the interesting corner: small places doing unusually strong work.

Excellenceshare of its work in the world top 10%, 2022-now and all time averaged
40%
Specialisationhow much of its work is in this field, counted up to 10× the world share
10%
Sizeits output in this field, on a log scale
30%
Growthoutput growth, counted from -20% to +20%
10%
Internationalshare of its work with a co-author abroad
10%
Each slider sets a weight; the share it gets of the score is beside it.
#UniversityScoreTop 10%SpecialisationWorksGrowth
1Brown UniversityUnited States 73.245.7%5.5×22 +31.9%
2Hong Kong Polytechnic UniversityChina 69.129.4%4.2×31 +645.3%
3ETH ZurichSwitzerland 65.321.3%7.0×41 +23.6%
4Northwestern Polytechnical UniversityChina 64.916.7%8.9×86 +146.0%
5Imperial College LondonUnited Kingdom 62.310.0%8.4×72 +122.2%
6Massachusetts Institute of TechnologyUnited States 62.215.2%8.3×49 +30.7%
7National University of SingaporeSingapore 59.919.6%3.4×34 +145.0%
8Stanford UniversityUnited States 58.518.3%3.3×42 +19.1%
9Tsinghua UniversityChina 58.414.6%3.7×73 +211.8%
10Xi'an Jiaotong UniversityChina 58.014.8%4.7×70 +143.5%

Universities only. The score blends excellence (40%), size (30%), specialisation (10%), growth (10%), international reach (10%), 2022-now; growth compares 2018-21 with 2022-25 and counts up to +20%, since a jump from a small base is mostly noise.

Every institution in Model Reduction and Neural Networks, country by country

Is Model Reduction and Neural Networks research growing?

Output in 2022-2025 was 108% higher than in 2018-2021, peaking in 2025. The fastest-growing topics are Model Reduction and Neural Networks.

still counting19801990200020102020
grewheldshrank

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

Its share of all research

Growing output can still be a shrinking share: all of science grows. This is Model Reduction and Neural Networks as a percentage of every work published that year, 0.033% in 2024.

still counting0.020%0.040%0.060%Model Reduction and Neural Networks0.046% in 202519801990200020102020

Fractional works of Model Reduction and Neural Networks over all fractional works that year. How the balance of science has shifted.

How much of it reaches the world top 10%

Year by year.

still counting5%10%15%Model Reduction and Neural Networks9.9% in 2025200020102020

Of each year's works in it, the share that reached the world's 10% most cited for their field and year. A field is the world for its own topics, so there is no other line to hold it against.

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.

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