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Volume 21, Issue 5
Automated Detection and Characterization of Singularities in Functions Using Neural Networks-From FFT Signals

Zheng Chen, Seulip Lee & Lin Mu

DOI: 10.4208/ijnam2024-1025

Int. J. Numer. Anal. Mod., 21 (2024), pp. 629-651.

Published online: 2024-10

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  • Abstract

Singularities, distinctive features signifying abrupt changes in function behavior, hold pivotal importance across numerous scientific disciplines. Accurate detection and characterization of these singularities are essential for understanding complex systems and performing data analysis. In this manuscript, we introduce a novel approach that employs neural networks and machine learning for the automated detection and characterization of singularities based on spectral data obtained through fast Fourier transform (FFT). Our methodology uses neural networks trained on known singular functions, along with the corresponding singularity information, to efficiently identify the location and characterize the nature of singularities within FFT data from arbitrary functions. Several tests have been provided to demonstrate the performance of our approach, including singularity detection for functions with single singularities and multiple singularities.

  • Keywords

Deep neural network, singularity detection, spectral data.

  • AMS Subject Headings

35A20, 35A21, 42A16, 42B05, 65T50

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-21-629, author = {Chen , ZhengLee , Seulip and Mu , Lin}, title = {Automated Detection and Characterization of Singularities in Functions Using Neural Networks-From FFT Signals}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2024}, volume = {21}, number = {5}, pages = {629--651}, abstract = {

Singularities, distinctive features signifying abrupt changes in function behavior, hold pivotal importance across numerous scientific disciplines. Accurate detection and characterization of these singularities are essential for understanding complex systems and performing data analysis. In this manuscript, we introduce a novel approach that employs neural networks and machine learning for the automated detection and characterization of singularities based on spectral data obtained through fast Fourier transform (FFT). Our methodology uses neural networks trained on known singular functions, along with the corresponding singularity information, to efficiently identify the location and characterize the nature of singularities within FFT data from arbitrary functions. Several tests have been provided to demonstrate the performance of our approach, including singularity detection for functions with single singularities and multiple singularities.

}, issn = {2617-8710}, doi = {https://doi.org/10.4208/ijnam2024-1025}, url = {http://global-sci.org/intro/article_detail/ijnam/23446.html} }
TY - JOUR T1 - Automated Detection and Characterization of Singularities in Functions Using Neural Networks-From FFT Signals AU - Chen , Zheng AU - Lee , Seulip AU - Mu , Lin JO - International Journal of Numerical Analysis and Modeling VL - 5 SP - 629 EP - 651 PY - 2024 DA - 2024/10 SN - 21 DO - http://doi.org/10.4208/ijnam2024-1025 UR - https://global-sci.org/intro/article_detail/ijnam/23446.html KW - Deep neural network, singularity detection, spectral data. AB -

Singularities, distinctive features signifying abrupt changes in function behavior, hold pivotal importance across numerous scientific disciplines. Accurate detection and characterization of these singularities are essential for understanding complex systems and performing data analysis. In this manuscript, we introduce a novel approach that employs neural networks and machine learning for the automated detection and characterization of singularities based on spectral data obtained through fast Fourier transform (FFT). Our methodology uses neural networks trained on known singular functions, along with the corresponding singularity information, to efficiently identify the location and characterize the nature of singularities within FFT data from arbitrary functions. Several tests have been provided to demonstrate the performance of our approach, including singularity detection for functions with single singularities and multiple singularities.

Chen , ZhengLee , Seulip and Mu , Lin. (2024). Automated Detection and Characterization of Singularities in Functions Using Neural Networks-From FFT Signals. International Journal of Numerical Analysis and Modeling. 21 (5). 629-651. doi:10.4208/ijnam2024-1025
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