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We combine the multigrid (MG) method with state-of-the-art concepts from the variational formulation of the numerical renormalization group. The resulting MG renormalization (MGR) method is a natural generalization of the MG method for…
Tensor ring (TR) decomposition has recently received increased attention due to its superior expressive performance for high-order tensors. However, the applicability of traditional TR decomposition algorithms to real-world applications is…
Real-world physical systems, like composite materials and porous media, exhibit complex heterogeneities and multiscale nature, posing significant computational challenges. Computational homogenization is useful for predicting macroscopic…
Dielectric tensor tomography (DTT) enables the reconstruction of three-dimensional (3D) dielectric tensors, which provides a physical measure of 3D optical anisotropy. Herein, we present a cost-effective and robust method for DTT…
We develop coarse-graining tensor renormalization group algorithms to compute physical properties of two-dimensional lattice models on finite periodic lattices. Two different coarse-graining strategies, one based on the tensor…
A fully tensorial theoretical framework for hypercomplex-valued neural networks is presented. The proposed approach enables neural network architectures to operate on data defined over arbitrary finite-dimensional algebras. The central…
This paper presents a multigrid algorithm for the computation of the rank-R canonical decomposition of a tensor for low rank R. Standard alternating least squares (ALS) is used as the relaxation method. Transfer operators and coarse-level…
Tomographic image sizes keep increasing over time and while the GPUs that compute the tomographic reconstruction are also increasing in memory size, they are not doing so fast enough to reconstruct the largest datasets. This problem is…
We consider the problem of low-rank decomposition of incomplete multiway tensors. Since many real-world data lie on an intrinsically low dimensional subspace, tensor low-rank decomposition with missing entries has applications in many data…
We introduce a family of numerical algorithms for the solution of linear system in higher dimensions with the matrix and right hand side given and the solution sought in the tensor train format. The proposed methods are rank--adaptive and…
Convolutional neural networks show outstanding results in a variety of computer vision tasks. However, a neural network architecture design usually faces a trade-off between model performance and computational/memory complexity. For some…
We introduce efficient solutions to optimize the cost of tree-like tensor network state method calculations when an expensive GPU-accelerated hardware is utilized. By supporting a main powerful compute node with additional auxiliary, but…
This paper presents a numerical framework for the low-rank approximation of the solution to three-dimensional parabolic problems. The key contribution of this work is the tensorization process based on a tensor-train reformulation of the…
We report a complete implementation of the coupled-cluster method with single, double, and triple excitations (CCSDT) where tensor decompositions are used to reduce its scaling and overall computational costs. For the decomposition of the…
We present efficient and scalable parallel algorithms for performing mathematical operations for low-rank tensors represented in the tensor train (TT) format. We consider algorithms for addition, elementwise multiplication, computing norms…
The state-of-the-art deep neural networks (DNNs) have been widely applied for various real-world applications, and achieved significant performance for cognitive problems. However, the increment of DNNs' width and depth in architecture…
We present a method for computing resonant inelastic x-ray scattering (RIXS) spectra in one-dimensional systems using the density matrix renormalization group (DMRG) method. By using DMRG to address the problem, we shift the computational…
The density matrix renormalization group (DMRG) algorithm is a popular alternating minimization scheme for solving high-dimensional optimization problems in the tensor train format. Classical DMRG, however, is based on sequential…
We discuss in detail algorithms for implementing tensor network renormalization (TNR) for the study of classical statistical and quantum many-body systems. Firstly, we recall established techniques for how the partition function of a 2D…
Tensor networks provide a useful tool to describe low-dimensional complex many-body systems. Finding efficient algorithms to use these methods for finite-temperature simulations in two dimensions is a continuing challenge. Here, we use the…