Tensor decompositions have emerged as powerful tools of multivariate data analysis, providing the foundation of numerous analysis methods. The Tucker decomposition in particular has been shown to be quite effective at compressing high-dimensional scientific datasets. However, applying these techniques to modern scientific simulation data is challenged by the massive data volumes these codes can produce, requiring scalable tensor decomposition methods that can exploit the hybrid parallelism available on modern computing architectures, as well as support in situ processing to compute decompositions as the data is being generated. In this work, we overcome these challenges by presenting a first-ever hybrid parallel and performance-portable approach for Tucker decomposition of both batch and streaming data. Our work is based on the TuckerMPI package, which provides scalable, distributed memory Tucker decomposition techniques, as well as prior work on a sequential streaming Tucker decomposition algorithm. We extend TuckerMPI to hybrid parallelism through the use of the Kokkos/Kokkos-Kernels performance portability packages, develop a hybrid parallel streaming Tucker decomposition algorithm, and demonstrate performance and portability of these approaches on a variety of large-scale scientific datasets on both CPU and GPU architectures.

In this paper, we present a new space-time Galerkin-like method, where we treat the discretization of spatial and temporal domains simultaneously. This method utilizes a mixed formulation of the tensor-train (TT) and quantized tensor-train (QTT) (please see Section Tensor-Train Decomposition), designed for the finite element discretization (Q1-FEM) of the time-dependent convection–diffusion–reaction (CDR) equation. We reformulate the assembly process of the finite element discretized CDR to enhance its compatibility with tensor operations and introduce a low-rank tensor structure for the finite element operators. Recognizing the banded structure inherent in the finite element framework’s discrete operators, we further exploit the QTT format of the CDR to achieve greater speed and compression. Additionally, we present a comprehensive approach for integrating variable coefficients of CDR into the global discrete operators within the TT/QTT framework. The effectiveness of the proposed method, in terms of memory efficiency and computational complexity, is demonstrated through a series of numerical experiments, including a semi-linear example.

Variational quantum algorithms (VQAs) are promising hybrid quantum-classical methods designed to leverage the computational advantages of quantum computing while mitigating the limitations of current noisy intermediate-scale quantum (NISQ) hardware. Although VQAs have been demonstrated as proofs of concept, their practical utility in solving real-world problems—and whether quantum-inspired classical algorithms can match their performance—remains an open question. We present a novel application of the variational quantum linear solver (VQLS) and its classical neural quantum states-based counterpart, the variational neural linear solver (VNLS), as key components within a minimum map Newton solver for a complementarity-based rigid-body contact model. We demonstrate using the VNLS that our solver accurately simulates the dynamics of rigid spherical bodies during collision events. These results suggest that quantum and quantum-inspired linear algebra algorithms can serve as viable alternatives to standard linear algebra solvers for modelling certain physical systems. This article is part of the theme issue ‘Numerical analysis, spectral graph theory, orthogonal polynomials and quantum algorithms’.