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Predicting the evolution of systems that exhibit spatio-temporal dynamics in response to external stimuli is a key enabling technology fostering scientific innovation. Traditional equations-based approaches leverage first principles to…
Unsupervised learning aims at the discovery of hidden structure that drives the observations in the real world. It is essential for success in modern machine learning. Latent variable models are versatile in unsupervised learning and have…
Networks of globally coupled, noise activated, bistable elements with connection time delays are considered. The dynamics of these systems is studied numerically using a Langevin description and analytically using (1) a Gaussian…
Monitoring high-dimensional engineering structures in extreme environments is limited by non-stationary excitation, nonlinear structural kinematics, and stochastic forcing. Traditional model-based and black-box data-driven methods often…
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…
In this article we introduce a broad family of adaptive, linear time-frequency representations termed superposition frames, and show that they admit desirable fast overlap-add reconstruction properties akin to standard short-time Fourier…
Operational forecasting centers are investing in decadal (1-10 year) forecast systems to support long-term decision making for a more climate-resilient society. One method that has previously been employed is the Dynamic Mode Decomposition…
This paper introduces an effective framework for designing memoryless dissipative full-state feedback for general linear delay systems via the Krasovski\u{i} functional (KF) approach, where an arbitrary finite number of pointwise and…
Modeling the evolution of system with time-series data is a challenging and critical task in a wide range of fields, especially when the time-series data is regularly sampled and partially observable. Some methods have been proposed to…
Dynamical systems with complex delayed interactions arise commonly when propagation times are significant, yielding complicated oscillatory instabilities. In this Letter, we introduce a class of systems with multiple, hierarchically long…
Modal decomposition techniques are important tools for the analysis of unsteady flows and, in order to provide meaningful insights with respect to coherent structures and their characteristic frequencies, the modes must possess a robust…
A new variational mode decomposition (VMD) based deep learning approach is proposed in this paper for time series forecasting problem. Firstly, VMD is adopted to decompose the original time series into several sub-signals. Then, a…
Dynamic mode decomposition (DMD) is an emerging methodology that has recently attracted computational scientists working on nonintrusive reduced order modeling. One of the major strengths that DMD possesses is having ground theoretical…
Representing and predicting high-dimensional and spatiotemporally chaotic dynamical systems remains a fundamental challenge in dynamical systems and machine learning. Although data-driven models can achieve accurate short-term forecasts,…
Parametric models deployed in non-stationary environments degrade as the underlying data distribution evolves over time (a phenomenon known as temporal domain drift). In the current work, we present KOMET (Koopman Operator identification of…
A computationally quick and conceptually simple method to recover time delay of the chaotic system from scalar time series is developed in this paper. We show that the orbits in the incomplete two-dimensional reconstructed phase-space will…
The problem of determining the underlying dynamics of a system when only given data of its state over time has challenged scientists for decades. In this paper, the approach of using machine learning to model the updates of the phase space…
Tensor decomposition of high-dimensional data often struggles to capture semantically or physically meaningful structures, particularly when relying on reconstruction objectives and fixed-rank constraints. We introduce a no-rank tensor…
The temporal dynamics of a complex system such as a social network or a communication network can be studied by understanding the patterns of link appearance and disappearance over time. A critical task along this understanding is to…
A kernel-based framework for spatio-temporal data analysis is introduced that applies in situations when the underlying system dynamics are governed by a dynamic equation. The key ingredient is a representer theorem that involves…