IPIA – Inverse Problems International Association

Welcome to the website of the Inverse Problems International Association (IPIA). 

IPIA aims to promote research in the field of Inverse Problems and to represent this field in the mathematical and scientific community as well as the general public. This is achieved by the organization and support of conferences, summer schools and prizes and by the distribution of pertinent information. In particular, IPIA coordinates the biannual Applied Inverse Problems (AIP) conferences and the Calderón prizes.

About Inverse Problems 

Inverse Problems is an interdisciplinary field of research concerned with the identification of quantities of interest from indirect observations. Inverse Problems in the natural sciences can often be described as finding causes for observed effects., e.g. finding a contrast function of the shape of a scattering obstacle from scattered waves in geophysical exploration, non-destructive testing or coherent diffractive imaging or finding an absorption coefficient from its Radon transform in computerized tomography.
Even if the unknown quantity is uniquely identified by ideal noise-free data, Inverse Problems are typically ill-posed in the sense that the solution does not depend continuously on the data. Then small measurement errors will cause huge errors in reconstructions unless prior information is exploited in the reconstruction process in some way, e.g. by the use of regularization techniques.
Research on Inverse Problems involves techniques from partial differential equations, differential geometry, data science, mathematical statistics, numerical analysis, optimization, imaging science, uncertainty quantification, and high performance computing, among others.   

About us

The Inverse Problems International Association was founded on May 10, 2022 as a registered non-profit society with seat in Göttingen, Germany. It is the successor of an informal society with the same name (see  http://www.inverseproblems.info/inverse_problems_international_association) that evolved from an initiative by Gunther Uhlmann and was founded at a conference in Japan in 2007.  
IPIA cooperates with regional inverse problems societies such as the Finnish Inverse Problems Society (FIPS), the German Speaking Inverse Problems Society (GIP), and the Eurasian Association on Inverse Problems (EAIP) as well as the Topical Activity Group on Inverse Problems of the European Mathematical Society