On the Optimal Linear Contraction Order of Tree Tensor Networks, and Beyond [PDF]
SIAM Journal on Scientific Computing, 2022 The contraction cost of a tensor network depends on the contraction order. However, the optimal contraction ordering problem is known to be NP-hard. We show that the linear contraction ordering problem for tree tensor networks admits a polynomial-time ...
Mihail Stoian +2 more
semanticscholar +1 more source
Effect of myofibre architecture on ventricular pump function by using a neonatal porcine heart model: from DT-MRI to rule-based methods [PDF]
Royal Society Open Science, 2020 Myofibre architecture is one of the essential components when constructing personalized cardiac models. In this study, we develop a neonatal porcine bi-ventricle model with three different myofibre architectures for the left ventricle (LV).
Debao Guan +3 more
doaj +1 more source
A condition for a perfect-fluid space-time to be a generalized Robertson-Walker space-time [PDF]
, 2016 A perfect-fluid space-time of dimension n>3 with 1) irrotational velocity vector field, 2) null divergence of the Weyl tensor, is a generalised Robertson-Walker space-time with Einstein fiber. Condition 1) is verified whenever pressure and energy density
De, Uday Chand +2 more
core +2 more sources
On the Decomposition of Tensors by Contraction [PDF]
Reviews of Modern Physics, 1949 The decomposition of tensors into irreducible representations of the orthogonal groups is calculated for three and four dimensions. The connection is shown with the problem of the allowed values of ordinary and isotopic spin for a given symmetry of the spacial eigenfunction of a nuclear system.
openaire +1 more source
Benchmarking treewidth as a practical component of tensor network simulations.
PLoS ONE, 2018 Tensor networks are powerful factorization techniques which reduce resource requirements for numerically simulating principal quantum many-body systems and algorithms.
Eugene F Dumitrescu +5 more
doaj +1 more source
Grassmann higher-order tensor renormalization group approach for two-dimensional strong-coupling QCD
Nuclear Physics B, 2023 We present a tensor-network approach for two-dimensional strong-coupling QCD with staggered quarks at nonzero chemical potential. After integrating out the gauge fields at infinite coupling, the partition function can be written as a full contraction of ...
Jacques Bloch, Robert Lohmayer
doaj +1 more source
Efficient Compilation of a Class of Variational Forms [PDF]
, 2007 We investigate the compilation of general multilinear variational forms over affines simplices and prove a representation theorem for the representation of the element tensor (element stiffness matrix) as the contraction of a constant reference tensor ...
Anders Logg +7 more
core +3 more sources
Improving the efficiency of variational tensor network algorithms [PDF]
, 2014 We present several results relating to the contraction of generic tensor networks and discuss their application to the simulation of quantum many-body systems using variational approaches based upon tensor network states.
Evenbly, Glen, Pfeifer, Robert N. C.
core +3 more sources
Distributed-memory multi-GPU block-sparse tensor contraction for electronic structure
IEEE International Parallel and Distributed Processing Symposium, 2020 Many domains of scientific simulation (chemistry, condensed matter physics, data science) increasingly eschew dense tensors for block-sparse tensors, sometimes with additional structure (recursive hierarchy, rank sparsity, etc.).
T. Hérault +6 more
semanticscholar +1 more source
High-Performance Tensor Contraction without Transposition [PDF]
SIAM Journal on Scientific Computing, 2016 Tensor computations---in particular tensor contraction (TC)---are important kernels in many scientific computing applications. Due to the fundamental similarity of TC to matrix multiplication and to the availability of optimized implementations such as ...
D. Matthews
semanticscholar +1 more source