Editing Inverse problem (section)

==Applications==
Inverse problem theory is used extensively in weather predictions, oceanography, hydrology, and petroleum engineering.<ref name="Wunsch1996">{{cite book| author=Carl Wunsch| title=The Ocean Circulation Inverse Problem| url=https://books.google.com/books?id=ugHsLF1RNacC&pg=PR9| date=13 June 1996| publisher=Cambridge University Press| isbn=978-0-521-48090-1|pages=9–}}</ref><ref>{{cite journal| last1=Tahmasebi|first1=Pejman| last2=Javadpour|first2=Farzam| last3=Sahimi|first3=Muhammad| title=Stochastic shale permeability matching: Three-dimensional characterization and modeling| journal=International Journal of Coal Geology| date=August 2016| volume=165| pages=231–242| doi=10.1016/j.coal.2016.08.024|bibcode=2016IJCG..165..231T }}</ref><ref>{{Cite journal| last1=Knighton|first1=James| last2=Singh|first2=Kanishka| last3=Evaristo|first3=Jaivime| date=2020| title=Understanding Catchment-Scale Forest Root Water Uptake Strategies Across the Continental United States Through Inverse Ecohydrological Modeling | journal=Geophysical Research Letters |language=en|volume=47|issue=1 | pages=e2019GL085937 | doi=10.1029/2019GL085937| bibcode=2020GeoRL..4785937K| s2cid=213914582| issn=1944-8007| doi-access=free}}</ref> Another application is inversion of elastic waves for non-destructive characterization of engineering structures.<ref name=":0">{{Cite journal |last1=Taslimian |first1=Rohollah |last2=Jaganathan |first2=Arun P. |date=2024 |title=Inversion of circumferential elastic waves for characterization of concrete pipes |journal=Wave Motion |language=en |volume=127 |pages=103272 |doi=10.1016/j.wavemoti.2024.103272|doi-access=free |bibcode=2024WaMot.12703272T }}</ref>

Inverse problems are also found in the field of heat transfer, where a surface heat flux<ref name="Figueiredo2014">{{cite book|author=Patric Figueiredo|title=Development Of An Iterative Method For Solving Multidimensional Inverse Heat Conduction Problems|url=https://www.academia.edu/9823088|date=December 2014|publisher=Lehrstuhl für Wärme- und Stoffübertragung RWTH Aachen}}{{Dead link|date=March 2024 |bot=InternetArchiveBot |fix-attempted=yes }}</ref> is estimated outgoing from temperature data measured inside a rigid body; and, in understanding the controls on plant-matter decay.<ref>{{Cite journal| last1=Forney|first1=David C.| last2=Rothman|first2=Daniel H.| date=2012-09-07 |title=Common structure in the heterogeneity of plant-matter decay |journal=Journal of the Royal Society Interface |volume=9|issue=74|pages=2255–2267 |doi=10.1098/rsif.2012.0122 |pmc=3405759 |pmid=22535699}}</ref> The linear inverse problem is also the fundamental of [[Spectral density estimation|spectral estimation]] and [[Direction of arrival|direction-of-arrival]] (DOA) estimation in [[signal processing]].

[[Inverse lithography]] is used in [[photomask]] design for [[semiconductor device fabrication]].