Component separation is one of the key stages of any modern, cosmic microwave background (CMB) data analysis pipeline. It is an inherently non-linear procedure and typically involves a series of sequential solutions of linear systems with similar, albeit not identical system matrices, derived for different data models of the same data set. Sequences of this kind arise for instance in the maximization of the data likelihood with respect to foreground parameters or sampling of their posterior distribution. However, they are also common in many other contexts. In this work we consider solving the component separation problem directly in the measurement (time) domain, which can have a number of important advantageous over the more standard pixel-based methods, in particular if non-negligible time-domain noise correlations are present as it is commonly the case. The time-domain based approach implies, however, significant computational effort due to the need to manipulate the full volume of time-domain data set. To address this challenge, we propose and study efficient solvers adapted to solving time-domain-based, component separation systems and their sequences and which are capable of capitalizing on information derived from the previous solutions. This is achieved either via adapting the initial guess of the subsequent system or through a so-called subspace recycling, which allows to construct progressively more efficient, two-level preconditioners. We report an overall speed-up over solving the systems independently of a factor of nearly 7, or 5, in the worked examples inspired respectively by the likelihood maximization and likelihood sampling procedures we consider in this work.
Proximal Implicit ODE Solvers for Accelerating Learning Neural ODEs
University of Utah（犹他大学）；University of California, Los Angeles（加州大学洛杉矶分校）；Illinois Institute of Technology（伊利诺伊理工学院）；University of California, Irvine（加州大学欧文分校）；Scientific Computing and Imaging (SCI) Institute（科学计算与成像研究所）
Quantifying Training Difficulty and Accelerating Convergence in Neural Network-Based PDE Solvers
Hong Kong University of Science and Technology（香港科技大学）；Shanghai Jiao Tong University（上海交通大学）；The Pennsylvania State University（宾夕法尼亚州立大学）；HKUST Shenzhen-Hong Kong Collaborative Innovation Research Institute（香港科技大学深港协同创新研究院）；Shanghai Artificial Intelligence Laboratory（上海人工智能实验室）
Opening the Blackbox: Accelerating Neural Differential Equations by Regularizing Internal Solver Heuristics
Indian Institute of Technology Kanpur（印度理工学院坎普尔分校）；Julia Computing；Massachusetts Institute of Technology（麻省理工学院）；University of Maryland Baltimore（马里兰大学巴尔的摩分校）；Pumas AI
Accelerating Natural Gradient Descent for PINNs with Randomized Numerical Linear Algebra
University of Pavia（帕维亚大学）；Department of Mathematics（数学系）；Department of Civil Engineering and Architecture（土木工程与建筑系）；Institut Camille Jordan, Lyon 1 Université（让·乔丹研究所，里昂1大学）
Accelerating Eigenvalue Dataset Generation via Chebyshev Subspace Filter
Department of Computer Science（计算机科学系）；Cranberry-Lemon University（Cranberry-Lemon 大学）；Department of Computational Neuroscience（计算神经科学系）；University of the Witwatersrand（沃图瓦特沃兹兰大学）；University of Science and Technology of China（中国科学技术大学）；CAS Key Laboratory of Technology in GIPAS, University of Science and Technology of China（中国科学技术大学GIPAS技术关键实验室）
