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.