相关论文: Data-driven model reduction and transfer operator …

We present a framework for constructing a structured realization of a linear time-invariant dynamical system solely from a discrete sampling of an input and output trajectory of the system. We estimate the transfer function of the original…

Fast and reliable surrogate models are critical for optimization, control and uncertainty analysis in geological carbon-storage projects, yet high-fidelity multiphase simulators remain too expensive. Dynamic Mode Decomposition (DMD) offers…

The present study focuses on a subject of significant interest in fluid dynamics: the identification of a model with decreased computational complexity from numerical code output using Koopman operator theory. A reduced-order modelling…

In recent years, algorithms aiming at learning models from available data have become quite popular due to two factors: 1) the significant developments in Artificial Intelligence techniques and 2) the availability of large amounts of data.…

We introduce a data-driven order reduction method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method rests on the assumption that the nonlinear system behaves…

We consider data-driven reduced-order models of partial differential equations with shift equivariance. Shift-equivariant systems typically admit traveling solutions, and the main idea of our approach is to represent the solution in a…

Model reduction methods aim to describe complex dynamic phenomena using only relevant dynamical variables, decreasing computational cost, and potentially highlighting key dynamical mechanisms. In the absence of special dynamical features…

Koopman operator theory shows how nonlinear dynamical systems can be represented as an infinite-dimensional, linear operator acting on a Hilbert space of observables of the system. However, determining the relevant modes and eigenvalues 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…

A new dimension reduction (DR) method for data sets is proposed by autonomous deforming of data manifolds. The deformation is guided by the proposed deforming vector field, which is defined by two kinds of virtual interactions between data…

Dimension reduction is often the first step in statistical modeling or prediction of multivariate spatial data. However, most existing dimension reduction techniques do not account for the spatial correlation between observations and do not…

This paper tackles the data-driven approximation of unknown dynamical systems using Koopman-operator methods. Given a dictionary of functions, these methods approximate the projection of the action of the operator on the finite-dimensional…

Data-driven model reduction methods provide a nonintrusive way of constructing computationally efficient surrogates of high-fidelity models for real-time control of soft robots. This work leverages the Lagrangian nature of the model…

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…

The Koopman operator and its data-driven approximations, such as extended dynamic mode decomposition (EDMD), are widely used for analysing, modelling, and controlling nonlinear dynamical systems. However, when the true Koopman…

Data-driven dimensionality reduction methods such as proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) have proven to be useful for exploring complex phenomena within fluid dynamics and beyond. A well-known…

We formulate extensions to Data Driven Computing for both distance minimizing and entropy maximizing schemes to incorporate time integration. Previous works focused on formulating both types of solvers in the presence of static equilibrium…

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…

We present parameter-interpolated dynamic mode decomposition (piDMD), a parametric reduced-order modeling framework that embeds known parameter-affine structure directly into the DMD regression step. Unlike existing parametric DMD methods…

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…