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Abstract <p>The numerical challenges of Tikhonov’s regularization method in solving general nonlinear problems are well known: non-uniqueness of the global extremum of the objective functional, high dimensionality and the need for extensive a priori information, the need to specify an initial approximation, determining the regularization parameter, etc. The use of neural network methods, in particular physics informed neural networks (PINNs), largely allows us to resolve these problems due to the ability to calculate a training sample of reference solutions (of virtually any desired dimensionality), decompose the original problem being solved, and apply special training methods adapted to the physics of the problem being solved. This paper provides a review and analyzes the experience of applying PINNs to solving nonlinear inverse problems of geoelectrics. It is noted that the first examples of constructing PINNs for solving inverse problems of geoelectrics were presented in a publication by the authors of this paper M.I. Shimelevich and E.A. Obornev in 2009. The problem of estimating the nonuniqueness (ambiguity) of the obtained solutions of inverse problems, which is insufficiently covered in the literature on geoelectrics, is considered separately.</p>

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Experience in Applying Physics-Informed Neural Networks to Inverse Problems of Geoelectrics

  • 期刊论文

  • 发表日期：

    2026年1月1日

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  • M. I. Shimelevich,
  • E. A. Obornev,
  • I. E. Obornev,
  • E. A. Rodionov

摘要

Abstract

The numerical challenges of Tikhonov’s regularization method in solving general nonlinear problems are well known: non-uniqueness of the global extremum of the objective functional, high dimensionality and the need for extensive a priori information, the need to specify an initial approximation, determining the regularization parameter, etc. The use of neural network methods, in particular physics informed neural networks (PINNs), largely allows us to resolve these problems due to the ability to calculate a training sample of reference solutions (of virtually any desired dimensionality), decompose the original problem being solved, and apply special training methods adapted to the physics of the problem being solved. This paper provides a review and analyzes the experience of applying PINNs to solving nonlinear inverse problems of geoelectrics. It is noted that the first examples of constructing PINNs for solving inverse problems of geoelectrics were presented in a publication by the authors of this paper M.I. Shimelevich and E.A. Obornev in 2009. The problem of estimating the nonuniqueness (ambiguity) of the obtained solutions of inverse problems, which is insufficiently covered in the literature on geoelectrics, is considered separately.