Andrei Chertkov, Gleb Ryzhakov, Georgii Novikov, Ivan Oseledets
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引用次数: 0
Abstract
The tensor train (TT) format, widely used in computational mathematics and machine learning, offers a computationally efficient method for handling multidimensional arrays, vectors, matrices, and discretized functions in various applications. In this article, we propose a new algorithm for estimating minimum/maximum elements of TT-tensors, which leads to accurate approximations. The method consists of sequential tensor multiplications of the TT-cores with an intelligent selection of candidates for the optimum. We propose a probabilistic interpretation of the method and estimate its complexity and convergence. We perform extensive numerical experiments with random tensors and various multivariable benchmark functions with the number of input dimensions up to 100. Our approach generates a solution close to the exact optimum for all model problems on a regular laptop.
期刊介绍：
Physics, medicine, astronomy -- these and other hard sciences share a common need for efficient algorithms, system software, and computer architecture to address large computational problems. And yet, useful advances in computational techniques that could benefit many researchers are rarely shared. To meet that need, Computing in Science & Engineering presents scientific and computational contributions in a clear and accessible format.
The computational and data-centric problems faced by scientists and engineers transcend disciplines. There is a need to share knowledge of algorithms, software, and architectures, and to transmit lessons-learned to a broad scientific audience. CiSE is a cross-disciplinary, international publication that meets this need by presenting contributions of high interest and educational value from a variety of fields, including—but not limited to—physics, biology, chemistry, and astronomy. CiSE emphasizes innovative applications in advanced computing, simulation, and analytics, among other cutting-edge techniques. CiSE publishes peer-reviewed research articles, and also runs departments spanning news and analyses, topical reviews, tutorials, case studies, and more.
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