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Subfield · Mathematics

Modeling and Simulation research

Modeling and Simulation is a subfield of Mathematics. Science Explorer counts 106k research works in it since 1950. 18.3% of them reached the world's top 10% most cited for their field and year.

In short: use of models – physical, mathematical, or otherwise logical representation of a system, entity, phenomenon, or process – as a basis for simulations – methods for implementing a model (either statically or) over time.

Research works
106k
fractional, since 1950
In the world top 10%
19k
per year above
Top-10% rate
18.3%
share of its works in the world top 10%
Topics
6
Growth, 2013–17 → 2018–22
+154%
the tick is no change

What is Modeling and Simulation research about, and what is growing?

By the world's output in 2019–23, its most used keywords are Modeling, COVID-19, transmission dynamics, Anomalous Diffusion, Fractional Calculus, Mathematical Modeling. Gaining share since 2009–13: COVID-19, transmission dynamics, Modeling. Losing share: Social Entrepreneurship, Space Exploration, Mathematical Modeling, Engineering Students.

▲ gaining share of this field◆ holding its share▼ losing share

Size is the world's fractional works in 2019–23 in the topics tagged with each word; colour compares the word's share of this field with 2009–13. Each links to the topic it comes from most.

All 14 words, with their numbers
  1. Modeling25k▲ 3.1×2 topics
  2. COVID-1925k▲ 3.2×1 topic
  3. transmission dynamics25k▲ 3.2×1 topic
  4. Anomalous Diffusion12k▼ 0.72×1 topic
  5. Fractional Calculus12k▼ 0.72×1 topic
  6. Mathematical Modeling4,182▼ 0.28×2 topics
  7. Cancer Growth3,564▼ 0.48×1 topic
  8. Tumor Invasion3,564▼ 0.48×1 topic
  9. Engineering Students840▼ 0.36×1 topic
  10. Mathematics Support840▼ 0.36×1 topic
  11. Social Entrepreneurship618▼ 0.08×1 topic
  12. Space Exploration618▼ 0.08×1 topic
  13. Interpolation139▼ 0.36×1 topic
  14. Mathematica139▼ 0.36×1 topic

Which countries lead Modeling and Simulation research?

On research quality in 2022–2025, the United States, China and India rank highest in Modeling and Simulation. By volume, China and the United States publish the most (4.6k and 3.8k works in 2022–2025).

By research quality, 2022–2025

  1. 1 United States · #1 all time 17.6% top 10% · 3.8k works
  2. 2 China · #2 all time 17.0% top 10% · 4.6k works
  3. 3 India · #4 all time 14.7% top 10% · 2.9k works
  4. 4 Saudi Arabia · #5 all time 26.2% top 10% · 1.1k works
  5. 5 United Kingdom · #3 all time 21.1% top 10% · 1k works
  6. 6 Pakistan · #13 all time 25.2% top 10% · 784 works
  7. 7 Italy · #7 all time 19.4% top 10% · 722 works
  8. 8 Türkiye · #10 all time 17.0% top 10% · 804 works
  9. 9 Egypt · #14 all time 26.7% top 10% · 435 works
  10. 10 Canada · #12 all time 18.5% top 10% · 552 works

The track on each row is that row’s top-10% rate. The ranking itself is the composite score, which the rate is only one part of.

Of 34 countries ranked in Modeling and Simulation. Composite of field-normalised excellence (50%), output (30%) and citations (20%); the bracket is the all-time rank.

All countries ranked in Modeling and Simulation

By volume, 2022–2025

  1. 1 China 4.6k works
  2. 2 United States 3.8k works
  3. 3 India 2.9k works
  4. 4 Saudi Arabia 1.1k works
  5. 5 United Kingdom 1k works
  6. 6 Türkiye 804 works
  7. 7 Pakistan 784 works
  8. 8 Italy 722 works
  9. 9 Iran 701 works
  10. 10 Nigeria 629 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: 27.1%United States: 22.4%India: 17.1%Saudi Arabia: 6.2%6 others listed: 27.2%27%largest
China4,622 · 27.1%United States3,824 · 22.4%India2,926 · 17.1%Saudi Arabia1,057 · 6.2%6 others listed4,651 · 27.2%

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

Which institutions lead Modeling and Simulation research?

Vellore Institute of Technology University (India) ranks first in Modeling and Simulation on research quality in 2022–2025, followed by Prince Sattam Bin Abdulaziz University and University of Oxford.

By research quality, 2022–2025

  1. 1 Vellore Institute of Technology University India · Vellore · #8 all time 31.8% top 10% · 111 works
  2. 2 Prince Sattam Bin Abdulaziz University Saudi Arabia · Al Kharj 38.1% top 10% · 70 works
  3. 3 University of Oxford United Kingdom · Oxford · #2 all time 25.9% top 10% · 68 works
  4. 4 Qassim University Saudi Arabia · Buraidah 25.7% top 10% · 63 works
  5. 5 King Abdulaziz University Saudi Arabia · Jeddah · #1 all time 23.1% top 10% · 90 works
  6. 6 King Saud University Saudi Arabia · Riyadh · #24 all time 19.2% top 10% · 86 works
  7. 7 Harbin Institute of Technology China · Harbin · #30 all time 16.9% top 10% · 64 works
  8. 8 Université Sultan Moulay Slimane Morocco · Beni Mellal 19.6% top 10% · 69 works
  9. 9 Centre National de la Recherche Scientifique France · Paris · #19 all time 15.9% top 10% · 66 works
  10. 10 University of North Carolina at Chapel Hill United States · Chapel Hill · #53 all time 4.5% top 10% · 95 works

The track on each row is that row’s top-10% rate. The ranking itself is the composite score, which the rate is only one part of.

Of 10 institutions above the floor of 40 fractional works in Modeling and Simulation.

Top 100 Modeling and Simulation institutions

By volume, 2022–2025

  1. 1 Vellore Institute of Technology UniversityIndia 111 works
  2. 2 University of North Carolina at Chapel HillUnited States 95 works
  3. 3 King Abdulaziz UniversitySaudi Arabia 90 works
  4. 4 King Saud UniversitySaudi Arabia 86 works
  5. 5 Prince Sattam Bin Abdulaziz UniversitySaudi Arabia 70 works
  6. 6 Université Sultan Moulay SlimaneMorocco 69 works
  7. 7 University of OxfordUnited Kingdom 68 works
  8. 8 Centre National de la Recherche ScientifiqueFrance 66 works
  9. 9 Harbin Institute of TechnologyChina 64 works
  10. 10 Qassim UniversitySaudi Arabia 63 works

Who are the leading researchers in Modeling and Simulation?

Among the most productive authors in Modeling and Simulation, Stanley Osher, Ziad A. Memish and Josep María Haro rank highest on the composite score.

  1. 1 Stanley Osher United States · #48 worldwide 8k citations · 207 works
  2. 2 Ziad A. Memish Saudi Arabia · #58 worldwide 5.3k citations · 162 works
  3. 3 Josep María Haro Spain · #63 worldwide 6.4k citations · 180 works
  4. 4 Simon I Hay United States · #67 worldwide 12k citations · 134 works
  5. 5 Martin McKee United Kingdom · #78 worldwide 5.4k citations · 369 works
  6. 6 Maarten J. Postma Netherlands · #90 worldwide 4.6k citations · 251 works
  7. 7 Alex Pentland United States · #100 worldwide 6k citations · 219 works
  8. 8 Till Bärnighausen Germany · #139 worldwide 5.4k citations · 123 works
  9. 9 George Em Karniadakis United States · #151 worldwide 6.3k citations · 268 works
  10. 10 Reinhard Busse Germany · #480 worldwide 3.1k citations · 103 works

Re-ranked on the composite score from the 3,754 highest-output authors in Modeling and Simulation. Identities come from OpenAlex author disambiguation, which occasionally merges or splits people.

Top 100 Modeling and Simulation researchers

Where is Modeling and Simulation research done?

The largest centres of Modeling and Simulation research in 2022–2025 are Beijing (China), London (United Kingdom), Riyadh (Saudi Arabia) and Shanghai (China). Among places with at least 20 works in it, it is an unusually large share of all research in Malakand, Beni Mellal and Osogbo.

Largest cities, 2022–2025

  1. 1 Beijing China 586 works
  2. 2 London United Kingdom 351 works
  3. 3 Riyadh Saudi Arabia 321 works
  4. 4 Shanghai China 296 works
  5. 5 Paris France 241 works
  6. 6 Moscow Russia 235 works
  7. 7 New Delhi India 222 works
  8. 8 Tehran Iran 221 works
  9. 9 Nanjing China 217 works
  10. 10 Guangzhou China 203 works

Where it is the local speciality

  1. MalakandPK · 44.5 works32×
  2. Beni MellalMA · 68.6 works17×
  3. OsogboNG · 35.1 works15×
← less than its size predicts1×more →

Location quotient: how much more of its research is in Modeling and Simulation than the world average.

See Modeling and Simulation on the map

Modeling and Simulation research by country

The best places for Modeling and Simulation research inside each country, with that country's researchers and world standing.

Where is the best place to study Modeling and Simulation?

Among universities, judged by research, Prince Sultan University, Prince Sattam Bin Abdulaziz University and China Medical 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%50%100%mean 39.94%fractional works in this node (log) →share in the world top 10% →Prince Sultan University: 56, 39.5%Prince Sattam Bin Abdulaziz University: 70, 38.1%China Medical University: 59, 39.5%University of Malakand: 44, 34.1%Lebanese American University: 58, 42.7%Imam Mohammad ibn Saud Islamic University: 58, 22.5%Abdul Wali Khan University Mardan: 27, 30.4%Al-Balqa Applied University: 30, 39.6%Near East University: 52, 38.7%Debre Berhan University: 16, 74.3%Prince Sultan Univer…China Medical Univer…Prince Sattam Bin Ab…University of Malakand
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 Prince Sultan UniversitySaudi Arabia 77.939.5%17.7×56 +994.7%
2 Prince Sattam Bin Abdulaziz UniversitySaudi Arabia 77.338.1%9.3×70 +660.0%
3 China Medical UniversityTaiwan 75.839.5%14.8×59 +367.0%
4 University of MalakandPakistan 71.634.1%31.9×44 +293.6%
5 Lebanese American UniversityLebanon 71.442.7%18.2×58 —
6 Imam Mohammad ibn Saud Islamic UniversitySaudi Arabia 68.722.5%10.8×58 +170.3%
7 Abdul Wali Khan University MardanPakistan 65.830.4%10.4×27 +232.9%
8 Al-Balqa Applied UniversityJordan 65.039.6%9.6×30 +181.2%
9 Near East UniversityCyprus 64.838.7%13.4×52 —
10 Debre Berhan UniversityEthiopia 64.374.3%14.8×16 —

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 Modeling and Simulation research growing?

Output in 2018–2022 was 154% higher than in 2013–2017, peaking in 2021. The fastest-growing topics are Fractional Differential Equations Solutions, COVID-19 epidemiological studies and Mathematical Biology Tumor Growth.

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.

  1. Fractional Differential Equations Solutions+176%
  2. COVID-19 epidemiological studies+173%
  3. Mathematical Biology Tumor Growth+85%
  4. Mathematics Education and Programs+54%
  5. Mathematical and Computational Methods+29%
  6. Advanced Research in Science and Engineering-67%
← shrinkingno changegrowing →

Growth in output from 2005–09 to 2015–19. Every topic is a page of its own.

What does Modeling and Simulation include?

COVID-19 epidemiological…40kCOVID-19 epidemiological studies: 40k fractional worksFractional Differential …37kFractional Differential Equations Solutions: 37k fractional worksMathematical Biology Tum…15kMathematical Biology Tumor Growth: 15k fractional worksAdvanced Research in Science and Engineering: 7,718 fractional worksMathematics Education and Programs: 5,694 fractional worksMathematical and Computational Methods: 1,134 fractional works

Area is fractional works in that topic. Every name below is a page of its own.