Artificial Neural Network-Based Computational Algorithm of Inverse Sumudu Transform Applied to Surface Transient Electromagnetic Sounding Method

Abstract

––The paper discusses the results of the development of a deep learning-based algorithm of the inverse Sumudu transform applied to the problem of on-ground non-stationary electromagnetic sounding. The Sumudu transform has potential for solving forward geoelectric problems in three-dimensional earth models because, unlike using the Laplace or Fourier transform, the Sumudu image of a real function is also a real function. Thus, there is no need to use complex numbers in subsequent calculations, which reduces computational costs and memory requirements in case of successful determination of the Sumudu image of the function. The disadvantages of the approach include the absence of an explicit method for calculating the inverse transform. The inversion can be done by solving the corresponding Fredholm integral equation of the first kind, but this is a poorly conditioned task leading to high requirements for the accuracy of the Sumudu image. The use of modern machine learning techniques can provide a method that is more robust to noise in the input data. This paper describes the process of creating a training dataset and developing a neural network algorithm; we evaluate the accuracy and performance of the obtained solution. The proposed method can contribute to the development of new approaches to physical processes modeling as well as to analysis, processing and interpretation of measured geophysical data.