Learning-Guided Integration Contours Construction for Fast Large-Scale Generalized Eigensolvers
arXiv:2511.01927v2 Announce Type: replace Abstract: Solving large-scale Generalized Eigenvalue Problems (GEPs) is a fundamental yet computationally prohibitive task in science and engineering. As a promising direction, contour integral (CI) methods offer an efficient and parallelizable framework. However, their performance is critically dependent on the selection of integration contours -- improper selection without reliable prior knowledge of eigenvalue distribution can incur significant computational overhead and compromise numerical accuracy. To address this challenge, we propose Deepcontou
The increasing scale and complexity of AI models and scientific simulations are driving demand for more efficient computational methods, making advancements in large-scale numerical solvers critically relevant.
Improved Generalized Eigenvalue Problem (GEP) solvers can significantly accelerate progress in fields like quantum chemistry, material science, and AI, which often rely on such complex computations.
The proposed 'Deepcontour' method, by optimizing integration contour selection using machine learning, could reduce computational overhead and improve accuracy for large-scale GEPs, making previously intractable problems manageable.
- · AI/ML researchers
- · Material scientists
- · Pharmaceutical industry
- · Supercomputing centers
- · Traditional numerical methods that are less scalable
- · Organizations without access to advanced computational resources
Faster solving of large-scale computational problems in scientific and engineering domains.
Acceleration of research and development cycles in areas dependent on high-performance computing, such as drug discovery and AI model training.
Potential for new scientific discoveries and technological breakthroughs enabled by the ability to simulate and analyze more complex systems.
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Read at arXiv cs.LG