کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4967372 | 1449372 | 2017 | 23 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Nearest-neighbor interaction systems in the tensor-train format
ترجمه فارسی عنوان
سیستم های تعامل نزدیکترین همسایه در فرمت تانسور-قطار
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
مهندسی کامپیوتر
نرم افزارهای علوم کامپیوتر
چکیده انگلیسی
Low-rank tensor approximation approaches have become an important tool in the scientific computing community. The aim is to enable the simulation and analysis of high-dimensional problems which cannot be solved using conventional methods anymore due to the so-called curse of dimensionality. This requires techniques to handle linear operators defined on extremely large state spaces and to solve the resulting systems of linear equations or eigenvalue problems. In this paper, we present a systematic tensor-train decomposition for nearest-neighbor interaction systems which is applicable to a host of different problems. With the aid of this decomposition, it is possible to reduce the memory consumption as well as the computational costs significantly. Furthermore, it can be shown that in some cases the rank of the tensor decomposition does not depend on the network size. The format is thus feasible even for high-dimensional systems. We will illustrate the results with several guiding examples such as the Ising model, a system of coupled oscillators, and a CO oxidation model.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational Physics - Volume 341, 15 July 2017, Pages 140-162
Journal: Journal of Computational Physics - Volume 341, 15 July 2017, Pages 140-162
نویسندگان
Patrick GelÃ, Stefan Klus, Sebastian Matera, Christof Schütte,