Methodology for Solving High-dimensional Multi-Parameter Inverse Problems of Indirect Measurements

Abstract

Inverse problems (IP) of indirect measurements are a class of IP encountered in most modern nature science experiments. Unfortunately, they are characterized by a number of properties making them hard to solve: they may be ill-posed or even incorrect, non-linear, and often they are characterized by high dimension by input and/or by output. As such, IP of indirect measurements require special methods to solve them. One of the classes of such methods are methods of machine learning (ML), which however possess special properties which should be taken into account when using them. In this paper, the authors suggest an outline of a special methodology, which can become the base for a standard scenario for processing data of indirect measurement IP with ML methods. The main notions underlying this methodology are also described and explained.