Related papers: Data-driven model reduction, Wiener projections, a…

Recently developed reduced-order modeling techniques aim to approximate nonlinear dynamical systems on low-dimensional manifolds learned from data. This is an effective approach for modeling dynamics in a post-transient regime where the…

We present a class of efficient parametric closure models for 1D stochastic Burgers equations. Casting it as statistical learning of the flow map, we derive the parametric form by representing the unresolved high wavenumber Fourier modes as…

In this paper we consider the problem of deriving approximate autonomous dynamics for a number of variables of a dynamical system, which are weakly coupled to the remaining variables. In a previous paper we have used the Ruelle response…

The hydrodynamics of thin films is typically described using phenomenological models whose connection to the microscopic particle dynamics is a subject of ongoing research. Existing methods based on density functional theory provide a good…

We present a comparative study of two methods for the reduction of the dimensionality of a system of ordinary differential equations that exhibits time-scale separation. Both methods lead to a reduced system of stochastic differential…

Derivation of reduced order representations of dynamical systems requires the modeling of the truncated dynamics on the retained dynamics. In its most general form, this so-called closure model has to account for memory effects. In this…

We examine the challenging problem of constructing reduced models for the long time prediction of systems where there is no timescale separation between the resolved and unresolved variables. In previous work we focused on the case where…

In this paper, we introduce a modular deep neural network (DNN) framework for data-driven reduced order modeling of dynamical systems relevant to fluid flows. We propose various deep neural network architectures which numerically predict…

Koopman analysis provides a general framework from which to analyze a nonlinear dynamical system in terms of a linear operator acting on an infinite-dimensional observable space. This theoretical framework provides a rigorous underpinning…

In this contribution, we discuss the modeling and model reduction framework known as the Loewner framework. This is a data-driven approach, applicable to large-scale systems, which was originally developed for applications to linear…

This paper introduces a method for data-driven control based on the Koopman operator model predictive control. Unlike exiting approaches, the method does not require a dictionary and incorporates a nonlinear input transformation, thereby…

Networks are landmarks of many complex phenomena where interweaving interactions between different agents transform simple local rule-sets into nonlinear emergent behaviors. While some recent studies unveil associations between the network…

A data-driven analysis method known as dynamic mode decomposition (DMD) approximates the linear Koopman operator on projected space. In the spirit of Johnson-Lindenstrauss Lemma, we will use random projection to estimate the DMD modes in…

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…

We present a data-driven nonintrusive model order reduction method for dynamical systems with moving boundaries. The proposed method draws on the proper orthogonal decomposition, Gaussian process regression, and moving least squares…

Dynamic mode decomposition (DMD) has emerged as a popular data-driven modeling approach to identifying spatio-temporal coherent structures in dynamical systems, owing to its strong relation with the Koopman operator. For dynamical systems…

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…

This paper presents a novel modeling approach for unsteady aircraft airflow, leveraging the Lorenz attractor framework. The proposed model is based on the force distribution exerted by a lift-generating wing on the surrounding fluid. It…

This work introduces a method for learning low-dimensional models from data of high-dimensional black-box dynamical systems. The novelty is that the learned models are exactly the reduced models that are traditionally constructed with model…

We propose a projection-based model order reduction method for the solution of parameter-dependent dynamical systems. The proposed method relies on the construction of time-dependent reduced spaces generated from evaluations of the solution…