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arXiv CS.AI·Jun 10·5 min read
Learning-Guided Integration Contours Construction for Fast Large-Scale Generalized Eigensolvers
TL;DR
Large-scale Generalized Eigenvalue Problems (GEPs) are computationally intensive, often hampered by poor contour selection for integration. Deepcontour, a hybrid framework combining a deep learning-based spectral predictor with Kernel Density Estimation (KDE), optimizes contour design for efficient eigenvalue extraction.
✦ Why It Matters
Engineers can leverage Deepcontour to significantly speed up eigenvalue computations in large-scale applications while ensuring accuracy.
Key Takeaways
- Utilize Deepcontour for faster eigenvalue problem solutions.
- Leverage deep learning for spectral distribution predictions.
- Incorporate Kernel Density Estimation for contour optimization.
- Achieve significant speedups while maintaining numerical accuracy.
How It Works
Deepcontour combines a deep learning model, the Eigen-Neural-Operator (ENO), with Kernel Density Estimation (KDE) to predict the spectral distribution of eigenvalues. This prediction informs the construction of optimized integration contours, which are crucial for the efficiency of contour integral methods in solving GEPs.
By automating contour design based on learned spectral information, Deepcontour significantly reduces computational overhead.