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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…
The conventional modal analysis techniques face difficulties in handling nonstationary phenomena, such as transient, nonperiodic, or intermittent phenomena. This paper presents a variational mode decomposition--based nonstationary coherent…
This paper presents FDNet: a Focal Decomposed Network for efficient, robust and practical time series forecasting. We break away from conventional deep time series forecasting formulas which obtain prediction results from universal feature…
Accurate traffic forecasting plays a vital role in intelligent transportation systems, enabling applications such as congestion control, route planning, and urban mobility optimization. However, traffic forecasting remains challenging due…
Time series forecasting is crucial for various applications, such as weather, traffic, electricity, and energy predictions. Currently, common time series forecasting methods are based on Transformers. However, existing approaches primarily…
Dynamic Mode Decomposition (DMD) is a numerical method that seeks to fit timeseries data to a linear dynamical system. In doing so, DMD decomposes dynamic data into spatially coherent modes that evolve in time according to exponential…
Dynamic mode decomposition (DMD) is a powerful data-driven technique for construction of reduced-order models of complex dynamical systems. Multiple numerical tests have demonstrated the accuracy and efficiency of DMD, but mostly for…
Dynamic mode decomposition (DMD) is a popular approach to analyzing and modeling fluid flows. In practice, datasets are almost always corrupted to some degree by noise. The vanilla DMD is highly noise-sensitive, which is why many…
Scientific research and engineering practice often require the modeling and decomposition of nonlinear systems. The Dynamic Mode Decomposition (DMD) is a novel Koopman-based technique that effectively dissects high-dimensional nonlinear…
Load forecasting plays a pivotal role in the safe and stable operation of power systems. Conventional deep learning methods often struggle to adapt to few-shot scenarios frequently encountered in industrial applications. Existing…
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…
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…
Many consequential real-world systems, like wind fields and ocean currents, are dynamic and hard to model. Learning their governing dynamics remains a central challenge in scientific machine learning. Dynamic Mode Decomposition (DMD)…
Existing techniques to encode spatial invariance within deep convolutional neural networks (CNNs) apply the same warping field to all the feature channels. This does not account for the fact that the individual feature channels can…
While the acquisition of time series has become more straightforward, developing dynamical models from time series is still a challenging and evolving problem domain. Within the last several years, to address this problem, there has been a…
Real-time forecasting from streaming data poses critical challenges: handling non-stationary dynamics, operating under strict computational limits, and adapting rapidly without catastrophic forgetting. However, many existing approaches face…
By investigating iterative methods for a constrained linear model, we propose a new class of fully connected V-cycle MgNet for long-term time series forecasting, which is one of the most difficult tasks in forecasting. MgNet is a CNN model…
Structural decoupling has played an essential role in model-based fault isolation and estimation in past decades, which facilitates accurate fault localization and reconstruction thanks to the diagonal transfer matrix design. However,…
Latent traversal is a popular approach to visualize the disentangled latent representations. Given a bunch of variations in a single unit of the latent representation, it is expected that there is a change in a single factor of variation of…
We present a data-driven method for separating complex, multiscale systems into their constituent time-scale components using a recursive implementation of dynamic mode decomposition (DMD). Local linear models are built from windowed…