Title: Accelerating Eigenvalue Dataset Generation via Chebyshev Subspace Filter
Primary area: applications to physical sciences (physics, chemistry, biology, etc.)
Keywords: Data Generation, Eigenvalue Problem, AI4PDE

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 **S**orting **C**hebyshev **S**ubspace **F**ilter (**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 (FFT) 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.