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Recently, large language models (LLMs) have demonstrated powerful capabilities in performing various tasks and thus are applied by recent studies to time series forecasting (TSF) tasks, which predict future values with the given historical…
A new method for analyzing high-dimensional categorical data, Linear Latent Structure (LLS) analysis, is presented. LLS models belong to the family of latent structure models, which are mixture distribution models constrained to satisfy the…
Time series data is a key element of big data analytics, commonly found in domains such as finance, healthcare, climate forecasting, and transportation. In large scale real world settings, such data is often high dimensional and…
Dynamic Linear Models (DLMs) are commonly employed for time series analysis due to their versatile structure, simple recursive updating, ability to handle missing data, and probabilistic forecasting. However, the options for count time…
Transformer-based and MLP-based methods have emerged as leading approaches in time series forecasting (TSF). While Transformer-based methods excel in capturing long-range dependencies, they suffer from high computational complexities and…
The development of efficient and robust dynamic models is fundamental in the field of systems and control engineering. In this paper, a new formulation for the dynamic model of nonlinear mechanical systems, that can be applied to different…
Large Language Models (LLMs) have emerged as a promising paradigm for time series analytics, leveraging their massive parameters and the shared sequential nature of textual and time series data. However, a cross-modality gap exists between…
Subsequence clustering of time series is an essential task in data mining, and interpreting the resulting clusters is also crucial since we generally do not have prior knowledge of the data. Thus, given a large collection of tensor time…
Power system time series analytics is critical in understanding the system operation conditions and predicting the future trends. Despite the wide adoption of Artificial Intelligence (AI) tools, many AI-based time series analytical models…
Dynamical system (DS)-based learning from demonstration (LfD) is a powerful tool for generating motion plans in the operation (`task') space of robotic systems. However, the realization of the generated motion plans is often compromised by…
Recently, there has been a growing interest in Long-term Time Series Forecasting (LTSF), which involves predicting long-term future values by analyzing a large amount of historical time-series data to identify patterns and trends. There…
Research on long-term time series prediction has primarily relied on Transformer and MLP models, while the potential of convolutional networks in this domain remains underexplored. To address this, we propose a novel multi-scale time series…
Based on its great successes in inference and denosing tasks, Dictionary Learning (DL) and its related sparse optimization formulations have garnered a lot of research interest. While most solutions have focused on single layer…
Current model structural discovery methods for power system dynamics impose rigid priors on the basis functions and variable sets of dynamic models while often neglecting algebraic constraints, thereby limiting the formulation of…
In this work, we present the novel mathematical framework of latent dynamics models (LDMs) for reduced order modeling of parameterized nonlinear time-dependent PDEs. Our framework casts this latter task as a nonlinear dimensionality…
The Dynamic-Mode Decomposition (DMD) is a well established data-driven method of finding temporally evolving linear-mode decompositions of nonlinear time series. Traditionally, this method presumes that all relevant dimensions are sampled…
Currently, machine learning (ML) methods are widely used to process the results of physical experiments. In some cases, due to the limited amount of experimental data, ML-models can be pre-trained on synthetic data simulated based on the…
In this paper, we provide a system theoretic treatment of a new class of multilinear time-invariant (MLTI) systems in which the states, inputs and outputs are tensors, and the system evolution is governed by multilinear operators. The MLTI…
In this study, we delve into the Structured State Space Model (S4), Change Point Detection methodologies, and the Switching Non-linear Dynamics System (SNLDS). Our central proposition is an enhanced inference technique and long-range…
In this article, we discuss some of the recent developments in applying machine learning (ML) techniques to nonlinear dynamical systems. In particular, we demonstrate how to build a suitable ML framework for addressing two specific…