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Topic · Mathematical Physics

Numerical methods in inverse problems

Numerical methods in inverse problems is a research topic within Mathematical Physics. Science Explorer counts 31k research works in it since 1950. 10.0% of them reached the world's top 10% most cited for their field and year.

This cluster of papers focuses on the mathematical theory and computational methods for solving inverse problems in various fields, including mathematical physics and imaging. It covers topics such as regularization methods, ill-posed problems, electrical impedance tomography, Calderón's problem, boundary value problems, inverse scattering theory, Tikhonov regularization, transmission eigenvalues, and numerical methods.

  • Inverse Problems
  • Regularization Methods
  • Ill-Posed Problems
  • Electrical Impedance Tomography
  • Calderón's Problem
  • Boundary Value Problem
  • Inverse Scattering Theory
  • Tikhonov Regularization
  • Transmission Eigenvalues
  • Numerical Methods
Research works
31k
fractional, since 1950
In the world top 10%
3.1k
per year above
Top-10% rate
10.0%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
+19%
the tick is no change
Largest producer
China
34% of the 10 largest, 2022-now
Numerical methods in inverse problems

Which countries lead Numerical methods in inverse problems research?

By volume, China and the United States publish the most (1.1k and 521 works in 2022-now).

By volume, 2022-now

  1. 1 China 1.1k works
  2. 2 United States 521 works
  3. 3 Russia 480 works
  4. 4 France 283 works
  5. 5 Italy 219 works
  6. 6 Germany 207 works
  7. 7 India 198 works
  8. 8 Japan 108 works
  9. 9 United Kingdom 96 works
  10. 10 Brazil 84 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: 34.1%United States: 15.6%Russia: 14.4%France: 8.5%6 others listed: 27.3%34%largest
China1,139 · 34.1%United States521 · 15.6%Russia480 · 14.4%France283 · 8.5%6 others listed912 · 27.3%

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

Which institutions lead Numerical methods in inverse problems research?

By volume in 2022-now, Russian Academy of Sciences publishes the most Numerical methods in inverse problems research, followed by Centre National de la Recherche Scientifique and Lomonosov Moscow State University.

By volume, 2022-now

  1. 1 Russian Academy of SciencesRussia 145 works
  2. 2 Centre National de la Recherche ScientifiqueFrance 129 works
  3. 3 Lomonosov Moscow State UniversityRussia 42 works
  4. 4 Chinese Academy of SciencesChina 35 works
  5. 5 St Petersburg UniversityRussia 24 works
  6. 6 Tsinghua UniversityChina 22 works
  7. 7 Harbin Institute of TechnologyChina 22 works
  8. 8 National Academy of Sciences of UkraineUkraine 22 works
  9. 9 Academy of Sciences Republic of UzbekistanUzbekistan 20 works
  10. 10 Beijing Institute of TechnologyChina 20 works

Who are the leading researchers in Numerical methods in inverse problems?

The most-cited researchers publishing on Numerical methods in inverse problems include John P. Perdew, Karl John Friston and Trevor Hastie.

  1. 1 John P. Perdew United States 436k citations
  2. 2 Karl John Friston United Kingdom 310k citations
  3. 3 Trevor Hastie United States 301k citations
  4. 4 Florian Fischer Germany 257k citations
  5. 5 R. W. L. Jones United Kingdom 189k citations
  6. 6 Michael I. Jordan United States 182k 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 Numerical methods in inverse problems?

The most cited paper in Numerical methods in inverse problems is "A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems" (Amir Beck, Marc Teboulle, 2009), with 12,347 citations. Next come "An iterative thresholding algorithm for linear inverse problems with a sparsity constraint" (5,044) and "Function minimization by conjugate gradients" (4,962).

Most cited papers
#PaperReleasedCitations
1 A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems Amir Beck, Marc Teboulle · SIAM Journal on Imaging Sciences 2009 12,347
2 An iterative thresholding algorithm for linear inverse problems with a sparsity constraint Ingrid Daubechies, Michel Defrise, Christine De Mol · Communications on Pure and Applied Mathematics 26 Aug 2004 5,044
3 Function minimization by conjugate gradients Roger Fletcher · The Computer Journal Feb 1964 4,962
4 A First-Order Primal-Dual Algorithm for Convex Problems with Applications to Imaging Antonin Chambolle, Thomas Pock · Journal of Mathematical Imaging and Vision 20 Dec 2010 4,454
5 The Use of the L-Curve in the Regularization of Discrete Ill-Posed Problems Per Christian Hansen, Dianne Prost O’Leary · SIAM Journal on Scientific Computing Nov 1993 3,155
All 100 most cited papers, with filters and sorting

Where is Numerical methods in inverse problems research done?

The largest centres of Numerical methods in inverse problems research in 2022-now are Beijing (China), Moscow (Russia), Paris (France) and Shanghai (China). Among places with at least 20 works in it, it is an unusually large share of all research in Bukhara.

Largest cities, 2022-now

  1. 1 BeijingChina 177 works
  2. 2 MoscowRussia 173 works
  3. 3 ParisFrance 82 works
  4. 4 ShanghaiChina 71 works
  5. 5 NanjingChina 62 works
  6. 6 Xi'anChina 46 works
  7. 7 NovosibirskRussia 45 works
  8. 8 TashkentUzbekistan 45 works
  9. 9 WuhanChina 44 works
  10. 10 Saint PetersburgRussia 44 works

Where it is the local speciality

  1. BukharaUZ · 21.7 works23×
← less than its size predicts1×more →

Location quotient: how much more of its research is in Numerical methods in inverse problems than the world average.

See Numerical methods in inverse problems on the map

Where is the best place to study Numerical methods in inverse problems?

Among universities, judged by research, City University of Hong Kong, Université Sultan Moulay Slimane and Chinese University of Hong Kong 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 20.04%fractional works in this field (log) →share of work in the world top 10% →Lanzhou University o…Université Sultan Mo…Chinese University o…City University of H…
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
1City University of Hong KongChina 70.817.8%6.6×16 +140.4%
2Université Sultan Moulay SlimaneMorocco 68.027.0%25.6×15 +341.3%
3Chinese University of Hong KongChina 58.319.6%3.2×10 +134.8%
4Lanzhou University of TechnologyChina 56.432.8%6.9×10 -3.2%
5Northwest Normal UniversityChina 56.216.8%17.4×18 +109.0%
6Bukhara State UniversityUzbekistan 56.010.6%64.9×20 +296.7%
7Jilin UniversityChina 54.423.4%3.3×16 +218.3%
8ETH ZurichSwitzerland 54.419.8%4.2×12 +54.2%
9Zhejiang Normal UniversityChina 52.319.1%9.6×12 +216.3%
10Tsinghua UniversityChina 52.113.5%2.2×22 +88.0%

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 Numerical methods in inverse problems, country by country

Is Numerical methods in inverse problems research growing?

Output in 2022-2025 was 19% higher than in 2018-2021, peaking in 2024. The fastest-growing topics are Numerical methods in inverse problems.

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 Numerical methods in inverse problems as a percentage of every work published that year, 0.023% in 2024.

still counting0.020%0.040%0.060%Numerical methods in inverse problems0.021% in 202519801990200020102020

Fractional works of Numerical methods in inverse problems 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%Numerical methods in inverse problems9.8% 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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