Related papers: Variational Mode Decomposition and Linear Embeddin…

Dynamic Mode Decomposition (DMD) is a model-order reduction approach, whereby spatial modes of fixed temporal frequencies are extracted from numerical or experimental data sets. The DMD low-rank or reduced operator is typically obtained by…

The DMD (Dynamic Mode Decomposition) method has attracted widespread attention as a representative modal-decomposition method and can build a predictive model. However, the DMD may give predicted results that deviate from physical reality…

Masked diffusion models have recently emerged as a flexible framework for discrete generative modeling. However, a key limitation of standard masked diffusion is its inability to effectively capture dependencies among tokens that are…

This work proposes a new framework of model reduction for parametric complex systems. The framework employs a popular model reduction technique dynamic mode decomposition (DMD), which is capable of combining data-driven learning and physics…

Reduced-order models have long been used to understand the behavior of nonlinear partial differential equations (PDEs). Naturally, reduced-order modeling techniques come at the price of computational accuracy for a decrease in computation…

The endeavor of stock trend forecasting is principally focused on predicting the future trajectory of the stock market, utilizing either manual or technical methodologies to optimize profitability. Recent advancements in machine learning…

Time series data is a prevalent form of data found in various fields. It consists of a series of measurements taken over time. Forecasting is a crucial application of time series models, where future values are predicted based on historical…

Simulating dynamics of open quantum systems is sometimes a significant challenge, despite the availability of various exact or approximate methods. Particularly when dealing with complex systems, the huge computational cost will largely…

Time series forecasting is a significant problem in many applications, e.g., financial predictions and business optimization. Modern datasets can have multiple correlated time series, which are often generated with global (shared)…

Time series data, including univariate and multivariate ones, are characterized by unique composition and complex multi-scale temporal variations. They often require special consideration of decomposition and multi-scale modeling to…

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…

We propose a new method for computing Dynamic Mode Decomposition (DMD) evolution matrices, which we use to analyze dynamical systems. Unlike the majority of existing methods, our approach is based on a variational formulation consisting of…

We have deluge of data in time series format for numerous phenomena. The number of snapshots, resolution and many other factors come into play as we look to identify the dynamics in a given problem. The pre-processing and post-processing…

Balanced data is required for deep neural networks (DNNs) when learning to perform power system stability assessment. However, power system measurement data contains relatively few events from where power system dynamics can be learnt. To…

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 an important application in various domains such as energy management, traffic planning, financial markets, meteorology, and medicine. However, real-time series data often present intricate temporal variability…

Short-term load forecasting is one of the crucial sections in smart grid. Precise forecasting enables system operators to make reliable unit commitment and power dispatching decisions. With the advent of big data, a number of artificial…

Time-series forecasting models often encounter abrupt changes in a given period of time which generally occur due to unexpected or unknown events. Despite their scarce occurrences in the training set, abrupt changes incur loss that…

In a number of environmental studies, relationships between natural processes are often assessed through regression analyses, using time series data. Such data are often multi-scale and non-stationary, leading to a poor accuracy of the…

Dynamic Mode Decomposition (DMD) yields a linear, approximate model of a system's dynamics that is built from data. We seek to reduce the order of this model by identifying a reduced set of modes that best fit the output. We adopt a model…