Accelerating Eigenvalue Dataset Generation via Chebyshev Subspace Filter

TL;DR

The paper introduces SCSF, a novel method that accelerates eigenvalue dataset generation by leveraging similarities between operators, achieving up to 3.5 times faster results than traditional solvers.

Contribution

SCSF is the first method to significantly speed up eigenvalue data generation by using operator similarities and Chebyshev filtering, reducing computational redundancy.

Findings

SCSF achieves up to 3.5x speedup over traditional solvers.

It leverages operator similarities to reduce redundant computations.

Experimental results validate the efficiency of SCSF.

Abstract

Eigenvalue problems are among the most important topics in many scientific disciplines. With the recent surge and development of machine learning, neural eigenvalue methods have attracted significant attention as a forward pass of inference requires only a tiny fraction of the computation time compared to traditional solvers. However, a key limitation is the requirement for large amounts of labeled data in training, including operators and their eigenvalues. To tackle this limitation, we propose a novel method, named Sorting Chebyshev Subspace Filter (SCSF), which significantly accelerates eigenvalue data generation by leveraging similarities between operators -- a factor overlooked by existing methods. Specifically, SCSF employs truncated fast Fourier transform sorting to group operators with similar eigenvalue distributions and constructs a Chebyshev subspace filter that leverages eigenpairs from previously solved problems to assist in solving subsequent ones, reducing redundant computations. To the best of our knowledge, SCSF is the first method to accelerate eigenvalue data generation. Experimental results show that SCSF achieves up to a 3.5 times speedup compared to various numerical solvers.