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Short-term industrial enterprises power system forecasting is an important issue for both load control and machine protection. Scientists focus on load forecasting but ignore other valuable electric-meters which should provide guidance of…

Embedded optimization-based planning for hybrid systems is challenging due to the use of mixed-integer programming, which is computationally intensive and often sensitive to the specific numerical formulation. To address that challenge,…

Multivariate time series data provide a robust framework for future predictions by leveraging information across multiple dimensions, ensuring broad applicability in practical scenarios. However, their high dimensionality and mixing…

General multivariate distributions are notoriously expensive to sample from, particularly the high-dimensional posterior distributions in PDE-constrained inverse problems. This paper develops a sampler for arbitrary continuous multivariate…

Higher-order tensors are becoming prevalent in many scientific areas such as computer vision, social network analysis, data mining and neuroscience. Traditional tensor decomposition approaches face three major challenges: model selecting,…

The so-called block-term decomposition (BTD) tensor model, especially in its rank-$(L_r,L_r,1)$ version, has been recently receiving increasing attention due to its enhanced ability of representing systems and signals that are composed of…

Time series forecasting in real world environments faces significant challenges non stationarity, multi scale temporal patterns, and distributional shifts that degrade model stability and accuracy. This study propose AdaMamba, a unified…

Multivariate time series forecasting involves predicting future values based on historical observations. However, existing approaches primarily rely on predefined single-scale patches or lack effective mechanisms for multi-scale feature…

We propose a Bayesian tensor-on-tensor regression approach to predict a multidimensional array (tensor) of arbitrary dimensions from another tensor of arbitrary dimensions, building upon the Tucker decomposition of the regression…

Tensor train (TT) decomposition provides a space-efficient representation for higher-order tensors. Despite its advantage, we face two crucial limitations when we apply the TT decomposition to machine learning problems: the lack of…

In this paper, we focus on the fixed TT-rank and precision problems of finding an approximation of the tensor train (TT) decomposition of a tensor. Note that the TT-SVD and TT-cross are two well-known algorithms for these two problems.…

Time Series Alignment is a critical task in signal processing with numerous real-world applications. In practice, signals often exhibit temporal shifts and scaling, making classification on raw data prone to errors. This paper introduces a…

This work proposes a novel general-purpose estimator for supervised machine learning (ML) based on tensor trains (TT). The estimator uses TTs to parametrize discretized functions, which are then optimized using Riemannian gradient descent…

Time series forecasting is crucial for various applications, such as weather, traffic, electricity, and energy predictions. Currently, common time series forecasting methods are based on Transformers. However, existing approaches primarily…

Multivariate Time Series (MTS) forecasting has a wide range of applications in both industry and academia. Recent advances in Spatial-Temporal Graph Neural Network (STGNN) have achieved great progress in modelling spatial-temporal…

This paper introduces a multiscale analysis based on optimal piecewise linear approximations of time series. An optimality criterion is formulated and on its base a computationally effective algorithm is constructed for decomposition of a…

We show how to build a multi-scale entanglement renormalization ansatz (MERA) representation of the ground state of a many-body Hamiltonian $H$ by applying the recently proposed \textit{tensor network renormalization} (TNR) [G. Evenbly and…

We investigate the application of tensor-train (TT) algorithms to multigroup thermal radiation transport (i.e., photon radiation transport). The TT framework enables simulations at discretizations that might otherwise be computationally…

The research related to digital twins has been increasing in recent years. Besides the mirroring of the physical word into the digital, there is the need of providing services related to the data collected and transferred to the virtual…

Approximating a tensor in the tensor train (TT) format has many important applications in scientific computing. Rounding a TT tensor involves further compressing a tensor that is already in the TT format. This paper proposes new randomized…