Principled Acceleration of Iterative Numerical Methods Using Machine Learning

Sohei Arisaka; Qianxiao Li

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arXiv · 2206.08594

Principled Acceleration of Iterative Numerical Methods Using Machine Learning

Sohei Arisaka·Qianxiao Li

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Abstract

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.

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Sohei Arisaka, Qianxiao Li. 2022-06-17. Principled Acceleration of Iterative Numerical Methods Using Machine Learning. https://arxiv.org/abs/2206.08594

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