相关论文: Data-driven resolvent analysis

A flow decomposition method based on canonical correlation analysis is proposed in this paper to optimally dissect complex flows into mutually orthogonal modes that are ranked by their cross-correlation with an observable. It is…

We present a novel approach to define the filter and relax steps in the evolve-filter-relax (EFR) framework for simulating turbulent flows. The EFR main advantages are its ease of implementation and computational efficiency. However, as it…

In this work, we investigate the use of data-driven equation discovery for dynamical systems to model and forecast continuous-time dynamics of unconstrained optimization problems. To avoid expensive evaluations of the objective function and…

Modeling complex dynamical systems under varying conditions is computationally intensive, often rendering high-fidelity simulations intractable. Although reduced-order models (ROMs) offer a promising solution, current methods often struggle…

The resolvent analysis reveals the worst-case disturbances and the most amplified response in a fluid flow that can develop around a stationary base state. The recent work by Padovan et al.(2020) extended the classical resolvent analysis to…

This paper describes a robust linear time-invariant output-feedback control strategy to reduce turbulent fluctuations, and therefore skin-friction drag, in wall-bounded turbulent fluid flows, that nonetheless gives performance guarantees in…

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…

The interaction between shear driven turbulence and stratification is a key process in a wide array of geophysical flows with spatio-temporal scales that span many orders of magnitude. A quick numerical model prediction based on external…

Numerical stabilization techniques are often employed in under-resolved simulations of convection-dominated flows to improve accuracy and mitigate spurious oscillations. Specifically, the evolve--filter--relax (EFR) algorithm is a framework…

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 derive the nonlinear equations satisfied by the coefficients of linear combinations that maximize their skewness when their variance is constrained to take a specific value. In order to numerically solve these nonlinear equations we…

The advent of big data has vast potential for discovery in natural phenomena ranging from climate science to medicine, but overwhelming complexity stymies insight. Existing theory is often not able to succinctly describe salient phenomena,…

To fully understand, analyze, and determine the behavior of dynamical systems, it is crucial to identify their intrinsic modal coordinates. In nonlinear dynamical systems, this task is challenging as the modal transformation based on the…

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…

Reduced-order models are indispensable for multi-query or real-time problems. However, there are still many challenges to constructing efficient ROMs for time-dependent parametrized problems. Using a linear reduced space is inefficient for…

In this effort we propose a data-driven learning framework for reduced order modeling of fluid dynamics. Designing accurate and efficient reduced order models for nonlinear fluid dynamic problems is challenging for many practical…

Because the Navier-Stokes equations are dissipative, the long-time dynamics of a flow in state space are expected to collapse onto a manifold whose dimension may be much lower than the dimension required for a resolved simulation. On this…

Stabilizing an unknown control system is one of the most fundamental problems in control systems engineering. In this paper, we provide a simple, model-free algorithm for stabilizing fully observed dynamical systems. While model-free…

Many real-world scientific processes are governed by complex nonlinear dynamic systems that can be represented by differential equations. Recently, there has been increased interest in learning, or discovering, the forms of the equations…

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…