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 - <p style="text-align: justify;">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.</p>