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Time Series Forecasting (TSF) is critical in many real-world domains like financial planning and health monitoring. Recent studies have revealed that Large Language Models (LLMs), with their powerful in-contextual modeling capabilities,…

An essential part of monitoring machine learning models in production is measuring input and output data drift. In this paper, we present a system for measuring distributional shifts in natural language data and highlight and investigate…

A framework is proposed to generate a phenomenological model that extracts the essence of a dynamical system (DS) with large degrees of freedom using machine learning. For a given microscopic DS, the optimum transformation to a small number…

Max-Plus Linear (MPL) systems are an algebraic formalism with practical applications in transportation networks, manufacturing and biological systems. In this paper, we investigate the problem of automatically analyzing the properties of…

In large-scale data processing scenarios, data often arrive in sequential streams generated by complex systems that exhibit drifting distributions and time-varying system parameters. This nonstationarity challenges theoretical analysis, as…

Multidimensional scaling (MDS) is a dimensionality reduction tool used for information analysis, data visualization and manifold learning. Most MDS procedures embed data points in low-dimensional Euclidean (flat) domains, such that…

We introduce a simple method to estimate the system parameters in continuous dynamical systems from the time series. In this method, we construct a modified system by introducing some constants (controlling constants) into the given…

Dynamic mode decomposition (DMD) is a data-driven method for estimating the dynamics of a discrete dynamical system. This paper proposes a tensor-based approach to DMD for applications in which the states can be viewed as tensors.…

Latent dynamics models have emerged as powerful tools for modeling and interpreting neural population activity. Recently, there has been a focus on incorporating simultaneously measured behaviour into these models to further disentangle…

Long-term time series forecasting (LTSF) is a crucial aspect of modern society, playing a pivotal role in facilitating long-term planning and developing early warning systems. While many Transformer-based models have recently been…

Within the field of complicated multivariate time series forecasting (TSF), popular techniques frequently rely on intricate deep learning architectures, ranging from transformer-based designs to recurrent neural networks. However, recent…

In this paper, we introduce a new adaptive data analysis method to study trend and instantaneous frequency of nonlinear and non-stationary data. This method is inspired by the Empirical Mode Decomposition method (EMD) and the recently…

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),…

Although pre-trained transformers and reprogrammed text-based LLMs have shown strong performance on time series tasks, the best-performing architectures vary widely across tasks, with most models narrowly focused on specific areas, such as…

Multivariate time series prediction has applications in a wide variety of domains and is considered to be a very challenging task, especially when the variables have correlations and exhibit complex temporal patterns, such as seasonality…

Dynamic Mode Decomposition (DMD) and its variants, such as extended DMD (EDMD), are broadly used to fit simple linear models to dynamical systems known from observable data. As DMD methods work well in several situations but perform poorly…

The decomposition of time series into components is an important task that helps to understand time series and can enable better forecasting. Nowadays, with high sampling rates leading to high-frequency data (such as daily, hourly, or…

Time series forecasting is prevalent in extensive real-world applications, such as financial analysis and energy planning. Previous studies primarily focus on time series modality, endeavoring to capture the intricate variations and…

Time-series prediction or forecasting is critical across many real-world dynamic systems, and recent studies have proposed using Large Language Models (LLMs) for this task due to their strong generalization capabilities and ability to…

The repetitive tracking task for time-varying systems (TVSs) with non-repetitive time-varying parameters, which is also called non-repetitive TVSs, is realized in this paper using iterative learning control (ILC). A machine learning (ML)…