{ANN-MoC method for the inverse problem of source characterization

Authors

DOI:

https://doi.org/10.5902/2179460X89819

Keywords:

Artificial neural network, Method of characteristics, Particle neutral transport, Inverse problem

Abstract

Inverse problems of neutral particle transport have significant applications in engineering and medicine. In this study, we present a new application of the ANN-MoC method to solve inverse problems of source characterization. It involves estimating the source parameters based on measurements of particle density at the boundaries of a one-dimensional computational domain. In summary, the method employs an artificial neural network (ANN) as a regression model. The neural network is trained using data generated from solutions of the method of characteristics (MoC) for the associated direct transport problem. Results of three test cases are presented. In the first, we highlight the advantage of preprocessing the input data. For all cases, sensibility tests are provided to study the advantages and limitations of the proposed approach in solving inverses problems with noisy data.

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Author Biographies

Nelson García Román, Universidade Federal do Rio Grande do Sul

Nelson García Román was born on September 20, 1992, in Pinar del Río, Cuba. He graduated as a Mechanical Engineer from the University of Pinar del Rio (2011-2016). During his studies, he was involved as a student assistant in Calculus and received two Honorable Mention awards for the presentation of two papers on Applied Mathematics in Engineering at the Scientific Conferences. After graduation, he became a professor at the same university from 2016 to 2018, and subsequently as a mathematics professor at the José Antonio Echeverría Technological University (CUJAE) until 2022. Currently, he is pursuing a Master's degree in the Graduate Program in Applied Mathematics (PPGMAp) at the Federal University of Rio Grande do Sul (UFRGS), where he holds a scholarship from CAPES, focusing on numerical methods, computational modeling, and deep learning for the numerical solution of particle neutral transport inverse problems.

Pedro Costa do Santos, Universidade Federal do Rio Grande do Sul

Pedro Costa dos Santos was born on September 23, 1998, in Rio de Janeiro - RJ, Brazil. During his secondary education, he successively received Honorable Mentions in the Brazilian Public School Mathematics Olympiad (OBMEP), and in 2015, he was awarded the Silver Medal in the competition. From 2016 to 2018, he attended an undergraduate course in Industrial Chemistry at the Federal University of Rio Grande do Sul(UFRGS). Since 2018, he has been a student in the undergraduate course of Applied Mathematics at UFRGS. Since 2022, he has been granted a scholarship for research initiation in Applied Mathematics, with an aim on Deep Learning applications to the numerical solution of Inverse Particle Neutral Transport problems. In 2023, he received the Honorable Mention for his research developments presented in the Scientific Initiation Week (SIC) at UFRGS.

Pedro Henrique de Almeida Konzen, Universidade Federal do Rio Grande do Sul

Pedro Henrique de Almeida Konzen was born on June 12, 1981, in Santa Cruz do Sul - RS, Brazil. Doctor in Applied Mathematics from the Federal University of Rio Grande do Sul (UFRGS, 2010), having conducted doctoral research at Ruprecht-Karls-Universität Heidelberg/Germany (Uni-HD, 2008-2010). Currently, Adjunct Professor at the Department of Pure and Applied Mathematics (DMPA), Institute of Mathematics and Statistics (IME), Federal University of Rio Grande do Sul (UFRGS, since 2014). Permanent member of the Graduate Program in Applied Mathematics (PPGMAp-UFRGS, since 2022). Has experience in the field of applied mathematics, with emphasis on numerical methods, computational simulation, mathematical modeling and deep learning.

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Published

2025-01-15

How to Cite

Román, N. G., do Santos, P. C., & Konzen, P. H. de A. (2025). {ANN-MoC method for the inverse problem of source characterization. Ciência E Natura, 47(esp. 1), e89819. https://doi.org/10.5902/2179460X89819

Issue

Vol. 47 No. esp. 1 (2025): IV Jornada de Matematica e Matematica aplicada UFSM

Section

IV Jornada de Matematica e Matematica aplicada UFSM

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