Аннотация:Inverse problems (IP) represent a very common class of problems that arise when processing experimental data. In fact, most problems of indirect measurement, used to determine some characteristics of the studied object, belong to this class. Unfortunately, many IP are incorrect or ill-conditioned, i.e. their solution is unstable or not unique. These properties greatly complicate the solution of such problems, and in the case of problems high-dimensional by input (measured data) and/or by output (object parameters) they make it virtually impossible, if the methods used are traditional mathematical methods based on operator matrix approach or on optimization algorithms.The alternative is to use adaptive nonlinear approximation methods, in particular, artificial neural networks (ANN). Thanks to their properties, such as resilience to noise and inconsistent data, and training by examples, ANN with the correct method of their application are able to carry out adaptive regularization of ill-posed problems, and often they are one of the most effective methods of their solution.This Chapter discusses the methodological aspects of the solution of IP with ANN. Various statements of IP from the point of view of used methods of data processing are given. Various methodological approaches to the solution of the IP when using neural network methods are considered, as well as their properties, differences and application areas. The differences of ANN from other methods of IP solution are discussed, and the main areas where their use is justified. The material is illustrated by high-dimensional IP from the areas of optical spectroscopy and exploration geophysics (electrical prospecting). Various approaches when solving multi-parameter IP are discussed: autonomous, simultaneous, group, and stepwise parameter determination.
