用相似算子加速求解特征值，生成数据快3.5倍
Accelerating Eigenvalue Dataset Generation via Chebyshev Subspace Filter
- 按特征值分布分组算子，复用已有解加速后续求解
- 相比传统求解器最高提速3.5倍，减少重复计算
- 适合需要大量特征值数据的机器学习训练场景
特征值问题是众多科学领域的核心内容。随着机器学习的发展，神经特征值方法因推理仅需极少计算量而受到关注，但其关键瓶颈在于训练需大量带标签数据（算子及其特征值）。为此，我们提出一种新方法——排序切比雪夫子空间滤波器（SCSF），通过利用算子间的相似性显著加速特征值数据生成。具体而言，SCSF采用截断快速傅里叶变换排序，将具有相似特征值分布的算子分组，并构建切比雪夫子空间滤波器，复用先前求解问题的特征对辅助后续求解，降低冗余计算。据我们所知，SCSF是首个实现特征值数据生成加速的方法。实验表明，相较于多种数值求解器，SCSF最高可提升3.5倍速度。
原文摘要 · Abstract (English)
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.
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