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In this paper, a novel decomposition method for non-stationary and nonlinear signals is proposed. This method is inspired by the adaptive wavelet filter bank of the empirical wavelet transform (EWT) and Fourier intrinsic band functions…

Dynamic mode decomposition (DMD) is a recently developed tool for the analysis of the behavior of complex dynamical systems. In this paper, we will propose an extension of DMD that exploits low-rank tensor decompositions of potentially…

Temporal non-stationarity, the phenomenon that time series distributions change over time, poses fundamental challenges to reliable time series forecasting. Intuitively, the complex time series can be decomposed into two factors, \ie…

The predictive advantage of combining several different predictive models is widely accepted. Particularly in time series forecasting problems, this combination is often dynamic to cope with potential non-stationary sources of variation…

We introduce a new adaptive decomposition tool, which we refer to as Nonlinear Mode Decomposition (NMD). It decomposes a given signal into a set of physically meaningful oscillations for any waveform, simultaneously removing the noise. NMD…

Time series forecasting holds significant value in various domains such as economics, traffic, energy, and AIOps, as accurate predictions facilitate informed decision-making. However, the existing Mean Squared Error (MSE) loss function…

Time series forecasting is crucial for many fields, such as disaster warning, weather prediction, and energy consumption. The Transformer-based models are considered to have revolutionized the field of sequence modeling. However, the…

Mobile edge computing (MEC) is considered as an efficient method to relieve the computation burden of mobile devices. In order to reduce the energy consumption and time delay of mobile devices (MDs) in MEC, multiple users multiple input and…

Time series foundation models (TSFMs) have recently achieved strong zero-shot forecasting performance through large-scale pretraining and retrieval-augmented prediction. However, our empirical analysis reveals a non-trivial limitation of…

Real-world time series are often governed by complex nonlinear dynamics. Understanding these underlying dynamics is crucial for precise future prediction. While deep learning has achieved major success in time series forecasting, many…

This paper considers the problem of signal decomposition and data visualization. For this purpose, we introduce a new multiscale transform, termed `ensemble patch transformation' that enhances identification of local characteristics…

Accurate mid-term (weeks to one year) hourly electricity load forecasts are essential for strategic decision-making in power plant operation, ensuring supply security and grid stability, planning and building energy storage systems, and…

The Ensemble Empirical Mode Decomposition (EEMD) has become a preferred technique to decompose nonlinear and non-stationary signals due to its ability to create time-varying basis functions. However, current EEMD signal cleaning techniques…

Accurately assessing the postmortem interval (PMI) is an important task in forensic science. Some of the existing techniques use regression models that use a decomposition score to predict the PMI or accumulated degree days (ADD), however,…

Multivariate or multichannel data have become ubiquitous in many modern scientific and engineering applications, e.g., biomedical engineering, owing to recent advances in sensor and computing technology. Processing these data sets is…

We introduce a comprehensive data-driven framework aimed at enhancing the modeling of physical systems, employing inference techniques and machine learning enhancements. As a demonstrative application, we pursue the modeling of cathodic…

Climate models, such as Earth system models (ESMs), are crucial for simulating future climate change based on projected Shared Socioeconomic Pathways (SSP) greenhouse gas emissions scenarios. While ESMs are sophisticated and invaluable,…

Modal analysis has long been consolidated as a basic tool to interpret dynamics and build low-order models of mechanical, thermal, and fluid systems. Eigenmodes arising from the spectral decomposition of the underlying linearized dynamics…

Experience of live video streaming can be improved if future available bandwidth can be predicted more accurately at the video uploader side. Thus follows a natural question which is how to make predictions both easily and precisely in an…

Dynamic mode decomposition (DMD), which the family of singular-value decompositions (SVD), is a popular tool of data-driven regression. While multiple numerical tests demonstrated the power and efficiency of DMD in representing data (i.e.,…