«Automation and Informatization of the fuel and energy complex»

Constructing a finite element approximation for the inverse problem solution using physics-informed neural networks

UDC: 517.9+519.6+004.032.26
DOI: -

Authors:

¹ National University of Oil and Gas "Gubkin University", Moscow, Russia

Keywords: physically informed neural networks (PINN), inverse problems, finite element approximations, domain decomposition (DD), deep learning (DL), full waveform inversion (FWI), wave equation, finite difference method, convolutional neural networks (CNN)

Annotation:

The authors of the article propose methods and algorithms for constructing a finite element approximation for the inverse coefficient problem solution using physics-informed neural networks. The key feature of the proposed approach is the independent prediction of a local approximation of the desired parameter by piecewise defined functions in each part of the decomposed domain using a trained neural network. Averaging of the coefficients for basic functions with a common vertex at the boundaries of the subdomains allows obtaining a continuous global coefficient and compensating errors within the region. The encoder is represented by a multi-layered convolutional architecture, created by analogy with EfficientNetV2. The possibilities of the proposed methods and algorithms were demonstrated on a synthetic data set of wave propagation described by an inhomogeneous two-dimensional wave equation with a variable speed coefficient. Synthetic solutions were obtained using the finite difference method. The advantages of using the described approach to the problem of full waveform inverse (FWI) are noted.

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