2022/06/17 by Sohei Arisaka, Arisaka, Sohei, Qianxiao Li +1 · 2 citations
Environmental Science · Physics and Astronomy · #65M06 #68T99 #68U20 #FOS: Computer and information sciences #FOS: Mathematics #Groundwater flow and contamination studies #Machine Learning (cs.LG) #Model Reduction and Neural Networks #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2206.08594
openalex publication_date 2022/06/17 · openalex created_date 2022/06/22 · openalex updated_date 2026/07/28
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.