Related papers: Global Optimization of Atomic Clusters via Physica…
Tensor networks developed in the context of condensed matter physics try to approximate order-$N$ tensors with a reduced number of degrees of freedom that is only polynomial in $N$ and arranged as a network of partially contracted smaller…
We propose an efficient implementation of the numerical tensor-train (TT) based algorithm solving the multicomponent coagulation equation preserving the nonnegativeness of solution. Unnatural negative elements in the constructed…
Density based representations of atomic environments that are invariant under Euclidean symmetries have become a widely used tool in the machine learning of interatomic potentials, broader data-driven atomistic modelling and the…
In the present work, the Tensor-Train decomposition algorithm is applied to reduce the memory footprint of a stochastic discrete velocity solver for rarefied gas dynamics simulation. An energy-conserving modification to the algorithm is…
Anticipating the low energy arrangements of atoms in space is an indispensable scientific task. Modern stochastic approaches to searching for these configurations depend on the optimisation of structures to nearby local minima in the energy…
Quantum computing and modern tensor-based computing have a strong connection, which is especially demonstrated by simulating quantum computations with tensor networks. The other direction is less studied: quantum computing is not often…
The tensor train rank (TT-rank) has achieved promising results in tensor completion due to its ability to capture the global low-rankness of higher-order (>3) tensors. On the other hand, recently, quaternions have proven to be a very…
We consider an approximate computation of several minimal eigenpairs of large Hermitian matrices which come from high--dimensional problems. We use the tensor train format (TT) for vectors and matrices to overcome the curse of…
We introduce compositional tensor trains (CTTs) for the approximation of multivariate functions, a class of models obtained by composing low-rank functions in the tensor-train format. This format can encode standard approximation tools,…
Tensor network contraction is central to problems ranging from many-body physics to computer science. We describe how to approximate tensor network contraction through bond compression on arbitrary graphs. In particular, we introduce a…
The implementation of adaptive genetic algorithms (AGA) for optimization problems has proven to be superior than many other methods due to its nature of producing more robust and high quality solutions. Considering the complexity involved…
The memory capacity of embedding tables in deep learning recommendation models (DLRMs) is increasing dramatically from tens of GBs to TBs across the industry. Given the fast growth in DLRMs, novel solutions are urgently needed, in order to…
In this paper, we explore the role of tensor algebra in balanced truncation (BT) based model reduction/identification for high-dimensional multilinear/linear time invariant systems. In particular, we employ tensor train decomposition (TTD),…
We apply a recently introduced method for global optimization to determine the ground state energy and configuration for model metallic clusters. The global minimum for a given N-atom cluster is found by following the damped dynamics of the…
This paper lies in the intersection of several fields: number theory, lattice theory, multilinear algebra, and scientific computing. We adapt existing solution algorithms for tensor eigenvalue problems to the tensor-train framework. As an…
Nonnegative Tucker decomposition (NTD) is a powerful tool for the extraction of nonnegative parts-based and physically meaningful latent components from high-dimensional tensor data while preserving the natural multilinear structure of…
The problem of incomplete data is common in signal processing and machine learning. Tensor completion algorithms aim to recover the incomplete data from its partially observed entries. In this paper, taking advantages of high…
Optimization of atomic structures presents a challenging problem, due to their highly rough and non-convex energy landscape, with wide applications in the fields of drug design, materials discovery, and mechanics. Here, we present a graph…
Low-rank Tucker and CP tensor decompositions are powerful tools in data analytics. The widely used alternating least squares (ALS) method, which solves a sequence of over-determined least squares subproblems, is costly for large and sparse…
Convex clustering is a modern clustering framework that guarantees globally optimal solutions and performs comparably to other advanced clustering methods. However, obtaining a complete dendrogram (clusterpath) for large-scale datasets…