ANN-MoC Method for Inverse Transient Transport Problems in One-Dimensional Domain

Nelson Garcia Roman; Pedro Costas dos Santos; Pedro Henrique de Almeida Konzen

Nelson Garcia Roman Universidade Federal de Rio Grande do Sul (UFRGS) https://orcid.org/0009-0006-8794-9500
Pedro Costas dos Santos Universidade Federal de Rio Grande do Sul (UFRGS) https://orcid.org/0009-0001-9927-2860
Pedro Henrique de Almeida Konzen Universidade Federal de Rio Grande do Sul (UFRGS) https://orcid.org/0000-0002-0411-1563

Keywords: artificial neural network, method of characteristics, particle neutral transport, inverse problem

Abstract

Transport problems of neutral particles have important applications in engineering and medical fields, from safety and quality protocols to optical medical procedures. In this paper, the ANN-MoC approach is proposed to solve the inverse transient transport problem of estimating the absorption coefficient from scalar flux measurements at the boundaries of the model domain. The central idea is to fit an Artificial Neural Network (ANN) using samples generated by direct solutions computed by a Method of Characteristics (MoC) solver. The direct solver validation is performed on a manufactured solution problem. Two inverse problems are then presented for testing the ANN-MoC method. In the first, a homogeneous medium is assumed, and, in the second, the medium is heterogeneous with a piecewise constant absorption coefficient. We show that the method can achieve good estimates, with accuracy depending on that of the direct solver. We also include a test of sensibility by studying the propagation of noise on the input data. The results highlight the potential of the proposed method to be applied to a broader range of inverse transport problems.

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