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A multiscale numerical solver called the seamless-domain method (SDM) is used in linear heat conduction analysis of nonperiodic simulated fields. The practical feasibility of the SDM has been verified for use with periodic fields but has…

We consider tensor data completion of an incomplete observation of multidimensional harmonic (MH) signals. Unlike existing tensor-based techniques for MH retrieval (MHR), which mostly adopt the canonical polyadic decomposition (CPD) to…

As an improvement of the Meshless Local Petrov-Galerkin (MLPG), the Direct Meshless Local Petrov-Galerkin (DMLPG) method is applied here to the numerical solution of transient heat conduction problem. The new technique is based on direct…

The aim of this work is to propose a new multiphysics mode synthesis (MMS) for the thermomechanical vibration problem. The present thermomechanical model is based on a state-space formulation, which consists of displacement, velocity, and…

This paper presents a goal-oriented a posteriori error estimation framework for linear functionals in the stabilized finite element discretization of the stationary convection-diffusion-reaction (CDR) equation. The theoretical framework for…

Many problems in computational neuroscience, neuroinformatics, pattern/image recognition, signal processing and machine learning generate massive amounts of multidimensional data with multiple aspects and high dimensionality. Tensors (i.e.,…

In the era of big data, effectively compressing large datasets while performing complex mathematical operations is crucial. Tensor-based decomposition methods have shown superior compression capabilities with minimal loss of accuracy…

Vector-matrix-multiplication (VMM) accel-erators have gained a lot of traction, especially due to therise of convolutional neural networks (CNNs) and the desireto compute them on the edge. Besides the classical digitalapproach, analog…

We present a new approach for the two-temperature molecular dynamics (MD) model for coupled simulations of electronic and phonon heat conduction in nanoscale systems. The proposed method uses a master equation to perform heat conduction of…

As the number of processor cores on supercomputers becomes larger and larger, algorithms with high degree of parallelism attract more attention. In this work, we propose a novel space-time coupled algorithm for solving an inverse problem…

In order to better understand micromechanical phenomena such as viscoelasticity and plasticity, the thermomechanical viewpoint is of prime importance but requires calorimetric measurements to be performed during a deformation process.…

This paper introduces an extended tensor decomposition (XTD) method for model reduction. The proposed method is based on a sparse non-separated enrichment to the conventional tensor decomposition, which is expected to improve the…

Dynamic Mode Decomposition (DMD) is a useful tool to effectively extract the dominant dynamic flow structure from a unsteady flow field. However, DMD requires massive computational resources with respect to memory consumption and the usage…

The dynamic mode decomposition (DMD) has become a leading tool for data-driven modeling of dynamical systems, providing a regression framework for fitting linear dynamical models to time-series measurement data. We present a simple…

A numerical algorithm for solving mantle convection problems with strongly variable viscosity is presented. Equations for conservation of mass and momentum for highly viscous and incompressible fluids are solved iteratively by a multigrid…

This article provides next step towards solving speed bottleneck of any system that intensively uses convolutions operations (e.g. CNN). Method described in the article is applied on deformable part models (DPM) algorithm. Method described…

Variational multiscale (VMS) methods offer a robust framework for handling under-resolved flow scales without resorting to problem-specific turbulence models. Here, we propose and assess a dynamic, term-by-term VMS stabilized formulation…

Existing algorithms with iterations as the principle for 3D inverse heat conduction problems (IHCPs) are usually time-consuming. With the recent advancements in deep learning techniques, it is possible to apply the neural network to compute…

The Hadamard decomposition is a powerful technique for data analysis and matrix compression, which decomposes a given matrix into the element-wise product of two or more low-rank matrices. In this paper, we develop an efficient algorithm to…

Multitask learning (MTL) can utilize the relatedness between multiple tasks for performance improvement. The advent of multimodal data allows tasks to be referenced by multiple indices. High-order tensors are capable of providing efficient…