Related papers: A Comparison of Parametric Dynamic Mode Decomposit…
We propose a method for learning dynamical systems from high-dimensional empirical data that combines variational autoencoders and (spatio-)temporal attention within a framework designed to enforce certain scientifically-motivated…
The performances of a new data processing technique, namely the Empirical Mode Decomposition, are evaluated on a fully developed turbulent velocity signal perturbed by a numerical forcing which mimics a long-period flapping. First, we…
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…
In part I of the article, we demonstrated that a variant of the Dynamic Mode Decomposition (DMD) algorithm based on variable projection optimization, called Optimized DMD (OPT-DMD), enables a robust identification of the dominant…
Reduced order models are computationally inexpensive approximations that capture the important dynamical characteristics of large, high-fidelity computer models of physical systems. This paper applies machine learning techniques to improve…
In this paper, we present a general numerical platform for designing accurate, efficient, and stable numerical algorithms for incompressible hydrodynamic models that obeys the thermodynamical laws. The obtained numerical schemes are…
Surrogate modelling is widely applied in computational science and engineering to mitigate computational efficiency issues for the real-time simulations of complex and large-scale computational models or for many-query scenarios, such as…
New explicit velocity- and position-Verlet-like algorithms of the second order are proposed to integrate the equations of motion in many-body systems. The algorithms are derived on the basis of an extended decomposition scheme at the…
This paper discusses the application of Dynamic Mode Decomposition (DMD) to the extraction of modal properties of linear mechanical systems, i.e., experimental modal analysis (EMA). First, theoretical background of the DMD is briefly…
Model reduction for fluid flow simulation continues to be of great interest across a number of scientific and engineering fields. Here, we explore the use of Neural Ordinary Differential Equations, a recently introduced family of…
Traffic flow forecasting is a crucial task in intelligent transport systems. Deep learning offers an effective solution, capturing complex patterns in time-series traffic flow data to enable the accurate prediction. However, deep learning…
The dynamics of many-body systems can often be captured in terms of only a few relevant variables. Mathematical and numerical approaches exist to identify these variables by exploiting a separation of time scales between slow relevant and…
Partial Differential Equations (PDEs) with high dimensionality are commonly encountered in computational physics and engineering. However, finding solutions for these PDEs can be computationally expensive, making model-order reduction…
This article presents the data-driven equation-free modeling of the dynamics of a hexafloat floating offshore wind turbine based on the application of dynamic mode decomposition (DMD). All the analyses are performed on experimental data…
Real-world systems often exhibit dynamics influenced by various parameters, either inherent or externally controllable, necessitating models capable of reliably capturing these parametric behaviors. Plasma technologies exemplify such…
Statistical tools are crucial for studying and modeling turbulent flows, where chaotic velocity fluctuations span a wide range of spatial and temporal scales. Advances in image velocimetry, especially in tracking-based methods, now allow…
The Dynamic Mode Decomposition (DMD) extracted dynamic modes are the non-orthogonal eigenvectors of the matrix that best approximates the one-step temporal evolution of the multivariate samples. In the context of dynamical system analysis,…
This study introduces and compares the Hankel dynamic mode decomposition with control (Hankel-DMDc) and a novel Bayesian extension of Hankel-DMDc as model-free (i.e., data-driven and equation-free) approaches for system identification and…
Training of neural networks is a computationally intensive task. The significance of understanding and modeling the training dynamics is growing as increasingly larger networks are being trained. We propose in this work a model based on the…
Computationally cheap yet accurate dynamical models are a key requirement for real-time capable nonlinear optimization and model-based control. When given a computationally expensive high-order prediction model, a reduction to a lower-order…