Related papers: Using matrix-product states for time-series machin…

We develop the methodology and a detailed case study in use of a class of Bayesian predictive synthesis (BPS) models for multivariate time series forecasting. This extends the recently introduced foundational framework of BPS to the…

Foundation MLIPs demonstrate broad applicability across diverse material systems and have emerged as a powerful and transformative paradigm in chemical and computational materials science. Equivariant MLIPs achieve state-of-the-art accuracy…

Irregular multivariate time series (IMTS) is characterized by the lack of synchronized observations across its different channels. In this paper, we point out that this channel-wise asynchrony can lead to poor channel-wise modeling of…

Temporal Point Processes (TPPs) are often used to represent the sequence of events ordered as per the time of occurrence. Owing to their flexible nature, TPPs have been used to model different scenarios and have shown applicability in…

This paper introduces a novel spatiotemporal feature representation model designed to address the limitations of traditional methods in multidimensional time series (MTS) analysis. The proposed approach converts MTS into one-dimensional…

An efficient numerical method is developed using the matrix product formalism for computing the properties at finite energy densities in one-dimensional (1D) many-body localized (MBL) systems. Arguing that any efficient (possibly quantum)…

We derived a number of numerical methods to treat biomolecular systems with multiple time scales. Based on the splitting of the operators associated with the slow-varying and fast-varying forces, new multiple time-stepping (MTS) methods are…

State-space models are successfully used in many areas of science, engineering and economics to model time series and dynamical systems. We present a fully Bayesian approach to inference \emph{and learning} (i.e. state estimation and system…

Multiple seasonal patterns play a key role in time series forecasting, especially for business time series where seasonal effects are often dramatic. Previous approaches including Fourier decomposition, exponential smoothing, and seasonal…

We introduce SeeMPS, a Python library dedicated to implementing tensor network algorithms based on the well-known Matrix Product States (MPS) and Quantized Tensor Train (QTT) formalisms. SeeMPS is implemented as a complete finite precision…

Machine Learning (ML) technologies have been increasingly adopted in Medical Cyber-Physical Systems (MCPS) to enable smart healthcare. Assuring the safety and effectiveness of learning-enabled MCPS is challenging, as such systems must…

Generation and analysis of time-series data is relevant to many quantitative fields ranging from economics to fluid mechanics. In the physical sciences, structures such as metastable and coherent sets, slow relaxation processes, collective…

The multi-layer multi-configuration time-dependent Hartree method (ML-MCTDH) is a highly efficient scheme for studying the dynamics of high-dimensional quantum systems. Its use is greatly facilitated if the Hamiltonian of the system…

Long Short-Term Memory (LSTM) is one of the most powerful sequence models. Despite the strong performance, however, it lacks the nice interpretability as in state space models. In this paper, we present a way to combine the best of both…

Reliable methods for the classification and quantification of quantum entanglement are fundamental to understanding its exploitation in quantum technologies. One such method, known as Separable Neural Network Quantum States (SNNS), employs…

The imputation of missing values in multivariate time series (MTS) data is critical in ensuring data quality and producing reliable data-driven predictive models. Apart from many statistical approaches, a few recent studies have proposed…

A considerable amount of clustering algorithms take instance-feature matrices as their inputs. As such, they cannot directly analyze time series data due to its temporal nature, usually unequal lengths, and complex properties. This is a…

We derive a criterion to determine when a translationally invariant matrix product state (MPS) has long-range localizable entanglement, where that quantity remains finite in the thermodynamic limit. We give examples fulfilling this…

Density matrix renormalization group (DMRG) or matrix product states (MPS) is the most effective and accurate method for studying one-dimensional quantum many-body systems. However, the application of DMRG to two-dimensional systems is not…

Subspace segmentation or subspace learning is a challenging and complicated task in machine learning. This paper builds a primary frame and solid theoretical bases for the minimal subspace segmentation (MSS) of finite samples. Existence and…