Numerical solution of the Molodensky boundary value problem with a fixed boundary

The functions of modern global navigation satellite systems (GNSS) allow us to consider the Earth’s surface as partially known at least. So, you can directly use the results of measurements on the real Earth surface, which significantly simplifies the entire theory of physical geodesy. The authors describe the theory of the Molodensky boundary value problem with a fixed boundary and its possible approximations briefly. It is proposed to look for a practical solution in the form of a deep neural network. Its choice represents a definite alternative to modern methods of physical geodesy and is of fundamental importance, since using neural networks with their unique flexibility and ability to learn from specific data enables significant expansion of computing capabilities and expecting the existence of a fairly reliable localized solution. In addition to theoretical considerations, the results of a numerical experiment to determine the high-frequency part of the disturbing potential in a local areа are described in detail