14 Facts About Inverse problems

Inverse problems are some of the most important mathematical problems in science and mathematics because they tell us about parameters that we cannot directly observe.

Field of inverse problems was later touched on by Soviet-Armenian physicist, Viktor Ambartsumian.

Nowadays inverse problems are investigated in fields outside physics, such as chemistry, economics, and computer science.

Inverse problems problem is the "inverse" of the forward problem: we want to determine the model parameters that produce the data that is the observation we have recorded.

Inverse problems are typically ill-posed, as opposed to the well-posed problems usually met in mathematical modeling.

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Many instances of regularized inverse problems can be interpreted as special cases of Bayesian inference.

Some inverse problems have a very simple solution, for instance, when one has a set of unisolvent functions, meaning a set of functions such that evaluating them at distinct points yields a set of linearly independent vectors.

Such Inverse problems include incomplete data for the x-ray transform in three dimensions and Inverse problems involving the generalisation of the x-ray transform to tensor fields.

Non-linear inverse problems constitute an inherently more difficult family of inverse problems.

Whereas linear inverse problems were completely solved from the theoretical point of view at the end of the nineteenth century, only one class of nonlinear inverse problems was so before 1970, that of inverse spectral and inverse scattering problems, after the seminal work of the Russian mathematical school.

Nonlinear inverse problems are currently studied in many fields of applied science.

Such inverse problems are of prime interest in seismology and exploration geophysics.

Inverse problems are found in the field of heat transfer, where a surface heat flux is estimated outgoing from temperature data measured inside a rigid body; and, in understanding the controls on plant-matter decay.

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