Deep Neural Networks for Singularity Detection

From Spectral Data

My collaborators and I have developed deep learning methods for detecting singularities in spectral data. We designed neural network architectures that infer both the location and exponent of singularities from only a small number of Fourier coefficients. These models achieve high accuracy even with multiple or hidden singularities, outperforming classical analytic techniques. Such detectors provide new tools for adaptive numerical simulation, as they identify regions that require mesh refinement or enriched discretizations, thereby helping to guide advanced PDE solvers more effectively.

Related Publications

• Z. Chen, S. Lee, and L. Mu, Automated detection and characterization of singularities in functions using neural networks-from FFT signals, International Journal of Numerical Analysis and Modeling, 21(5) (2024) 629-651.