Principled Acceleration of Iterative Numerical Methods Using Machine Learning
This work addresses the challenge of efficiently accelerating large-scale scientific computing applications, though it appears incremental as it builds on prior learning-based acceleration methods.
The paper tackles the problem of accelerating iterative numerical methods using machine learning by analyzing existing approaches and identifying a departure from classical meta-learning that can degrade performance. It introduces a novel training method that theoretically improves upon existing methods and demonstrates significant advantages in various numerical applications.
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.