Iterative methods are ubiquitous in large-scale scientific computing applications, and a number of approaches based on meta-learning have been recently proposed to accelerate them. However, a systematic study of these approaches and how they differ from meta-learning is lacking. In this paper, we propose a framework to analyze such learning-based acceleration approaches, where one can immediately identify a departure from classical meta-learning. We show that this departure may lead to arbitrary deterioration of model performance. Based on our analysis, we introduce a novel training method for learning-based acceleration of iterative methods. Furthermore, we theoretically prove that the proposed method improves upon the existing methods, and demonstrate its significant advantage and versatility through various numerical applications.

翻译：迭代方法在大规模科学计算应用中无处不在，近期基于元学习的方法被提出以加速此类计算。然而，目前缺乏对这些方法及其与元学习差异的系统性研究。本文提出一个分析此类基于学习的加速方法的框架，可立即识别出它们与经典元学习的本质分野。我们论证这种分野可能导致模型性能的任意劣化。基于分析结果，我们提出一种用于加速迭代方法的创新训练方法。此外，我们从理论上证明该方法优于现有方案，并通过多种数值应用验证了其显著优势与广泛适用性。