2024-05-22 ロスアラモス国立研究所(LANL)
The mixed tensor train (TT) and quantized tensor train (QTT) method was shown to perform with exceptional efficiency, speed, and memory, along with a record yottabyte data compression.
◆研究チームは、テンソルトレイン（TT）と量子化テンソルトレイン（QTT）を組み合わせて三次元のボルツマン中性子輸送方程式を解決し、標準的なデスクトップコンピュータ上でテラバイトサイズのデータをメガバイトに圧縮しました。これにより、従来の方法よりも効率的かつ高速でメモリ使用量も少ないことを証明しました。今後、複数材料の問題や非線形の中性子輸送方程式への応用が期待されています。
＜関連情報＞
- https://discover.lanl.gov/news/0513-tensor-network-approach/
- https://www.sciencedirect.com/science/article/pii/S002199912400192X?via%3Dihub
時間非依存ボルツマン中性子輸送方程式を解くテンソルネットワーク Tensor networks for solving the time-independent Boltzmann neutron transport equation
Duc P. Truong, Mario I. Ortega, Ismael Boureima, Gianmarco Manzini, Kim Ø. Rasmussen, Boian S. Alexandrov
Journal of Computational Physics Available online 19 March 2024
DOI:https://doi.org/10.1016/j.jcp.2024.112943
Abstract
Tensor network techniques, known for their low-rank approximation ability that breaks the curse of dimensionality, are emerging as a foundation of new mathematical methods for ultra-fast numerical solutions of high-dimensional Partial Differential Equations (PDEs). Here, we present a mixed Tensor Train (TT)/Quantized Tensor Train (QTT) approach for the numerical solution of time-independent Boltzmann Neutron Transport equations (BNTEs) in Cartesian geometry. Discretizing a realistic three-dimensional (3D) BNTE by (i) diamond differencing in space,() multigroup-in-energy, and () discrete ordinates collocation in angle leads to large generalized eigenvalue problems that generally require a matrix-free approach and large computer clusters. Starting from this discretization, we construct a TT representation of the PDE fields and discrete operators, followed by a QTT representation of the TT cores. We then solve the tensorized generalized eigenvalue problem using a fixed-point scheme with tensor network optimization techniques. We validate our approach by applying the method to two examples of 3D neutron transport problems, currently solved by the Los Alamos National Laboratory PARallel TIme-dependent SN (PARTISN) solver.1 We demonstrate that our TT/QTT method, executed on a standard desktop computer, leads to large compression. This allows for the storage of terrabyte-sized neutron angular flux eigenvectors in megabytes. Additionally, we create megabyte-sized full access TT representations of yottabyte-sized transport matrix operators. By leveraging the TT operators and solution methods, we obtain a 7500 times speedup when compared to the PARTISN solution time with an error of less than 10−5.
