Related papers: A Splitting Approach to Dynamic Mode Decomposition…

This paper presents a novel adaptive-sparse polynomial dimensional decomposition (PDD) method for stochastic design optimization of complex systems. The method entails an adaptive-sparse PDD approximation of a high-dimensional stochastic…

Dynamic Mode Decomposition (DMD) is a data-driven modeling tool that generates a model from spatio-temporal data. The data needs to be as clean as possible for DMD to come up with a faithful model. We review a few data-filtering methods to…

Dynamic mode decomposition (DMD) is a data-driven technique used for capturing the dynamics of complex systems. DMD has been connected to spectral analysis of the Koopman operator, and essentially extracts spatial-temporal modes of the…

We develop a novel deep learning technique, termed Deep Orthogonal Decomposition (DOD), for dimensionality reduction and reduced order modeling of parameter dependent partial differential equations. The approach consists in the construction…

Solving optimal control problems for transport-dominated partial differential equations (PDEs) can become computationally expensive, especially when dealing with high-dimensional systems. To overcome this challenge, we focus on developing…

Dynamic mode decomposition (DMD) is a popular data-driven framework to extract linear dynamics from complex high-dimensional systems. In this work, we study the system identification properties of DMD. We first show that DMD is invariant…

The Dynamic Mode Decomposition (DMD) is a tool of trade in computational data driven analysis of fluid flows. More generally, it is a computational device for Koopman spectral analysis of nonlinear dynamical systems, with a plethora of…

Dynamic Mode Decomposition (DMD) and its variants, such as extended DMD (EDMD), are broadly used to fit simple linear models to dynamical systems known from observable data. As DMD methods work well in several situations but perform poorly…

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…

We propose in this paper an adaptive reduced order modelling technique based on domain partitioning for parametric problems of fracture. We show that coupling domain decomposition and projection-based model order reduction permits to focus…

We develop new dynamically orthogonal tensor methods to approximate multivariate functions and the solution of high-dimensional time-dependent nonlinear partial differential equations (PDEs). The key idea relies on a hierarchical…

We propose a new approach to learning the subgrid-scale model when simulating partial differential equations (PDEs) solved by the method of lines and their representation in chaotic ordinary differential equations, based on neural ordinary…

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…

In this paper we consider the problem of distributed nonlinear optimisation of a separable convex cost function over a graph subject to cone constraints. We show how to generalise, using convex analysis, monotone operator theory and…

This paper introduces an adaptive time splitting technique for the solution of stiff evolutionary PDEs that guarantees an effective error control of the simulation, independent of the fastest physical time scale for highly unsteady…

High dimensional and/or nonconvex optimization remains a challenging and important problem across a wide range of fields, such as machine learning, data assimilation, and partial differential equation (PDE) constrained optimization. Here we…

Dynamic mode decomposition (DMD) is a data-driven method for estimating the dynamics of a discrete dynamical system. This paper proposes a tensor-based approach to DMD for applications in which the states can be viewed as tensors.…

The simulation of atmospheric flows by means of traditional discretization methods remains computationally intensive, hindering the achievement of high forecasting accuracy in short time frames. In this paper, we apply three reduced order…

In this work, we consider wave propagation in materials characterized by nonlinear properties or damage. To accelerate the simulations of the resulting high-dimensional problems, we apply model order reduction methods. Depending on the…

Projection-based reduced order models are effective at approximating parameter-dependent differential equations that are parametrically separable. When parametric separability is not satisfied, which occurs in both linear and nonlinear…