Learning-Guided Integration Contours Construction for Fast Large-Scale Generalized Eigensolvers

The paper introduces Deepcontour, a novel hybrid framework that combines deep learning with Kernel Density Estimation (KDE) to optimize integration contours for Generalized Eigenvalue Problems (GEPs). Utilizing an Eigen-Neural-Operator (ENO) for rapid spectral predictions, Deepcontour achieves up to a 5.63x speedup in computational efficiency while preserving numerical accuracy. This approach is significant for practitioners as it enhances the performance of contour integral methods in solving large-scale GEPs, facilitating more efficient computations in scientific and engineering applications.