Data-driven resolvent analysis

Abstract

Resolvent analysis identifies the most responsive forcings and most receptive states of a dynamical system, in an input--output sense, based on its governing equations. Interest in the method has continued to grow during the past decade due to its potential to reveal structures in turbulent flows, to guide sensor/actuator placement, and for flow control applications. However, resolvent analysis requires access to high-fidelity numerical solvers to produce the linearized dynamics operator. In this work, we develop a purely data-driven algorithm to perform resolvent analysis to obtain the leading forcing and response modes, without recourse to the governing equations, but instead based on snapshots of the transient evolution of linearly stable flows. The formulation of our method follows from two established facts: $1)$ dynamic mode decomposition can approximate eigenvalues and eigenvectors of the underlying operator governing the evolution of a system from measurement data, and $2)$ a projection of the resolvent operator onto an invariant subspace can be built from this learned eigendecomposition. We demonstrate the method on numerical data of the linearized complex Ginzburg--Landau equation and of three-dimensional transitional channel flow, and discuss data requirements. The ability to perform resolvent analysis in a completely equation-free and adjoint-free manner will play a significant role in lowering the barrier of entry to resolvent research and applications.

References in corpus (29)

• Discovering governing equations from data: Sparse identification of nonlinear dynamical systems
• Machine Learning for Fluid Mechanics
• A Data-Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition
• On Dynamic Mode Decomposition: Theory and Applications
• Turbulence Modeling in the Age of Data
• Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis
• Sparsity-promoting dynamic mode decomposition
• A critical layer model for turbulent pipe flow
• Spectral analysis of jet turbulence
• Visualizing the geometry of state space in plane Couette flow
• Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systems
• Dynamic Mode Decomposition for Large and Streaming Datasets
• Resolvent-analysis-based design of airfoil separation control
• Model-based scaling of the streamwise energy density in high-Reynolds number turbulent channels
• Modeling of Transitional Channel Flow Using Balanced Proper Orthogonal Decomposition
• Randomized Dynamic Mode Decomposition
• Toward compressed DMD: spectral analysis of fluid flows using sub-Nyquist-rate PIV data
• From bypass transition to flow control and data-driven turbulence modeling: An input-output viewpoint
• Resolvent-based modelling of coherent wavepackets in a turbulent jet
• Compressed Dynamic Mode Decomposition for Background Modeling
• A reduced-order model of three-dimensional unsteady flow in a cavity based on the resolvent operator
• A low-order decomposition of turbulent channel flow via resolvent analysis and convex optimization
• Non-linear input/output analysis: application to boundary layer transition
• Randomized resolvent analysis
• Cluster-based network model
• Efficient computation of global resolvent modes
• Analysis of amplification mechanisms and cross-frequency interactions in nonlinear flows via the harmonic resolvent
• Artificial eigenmodes in truncated flow domains
• Learning the Tangent Space of Dynamical Instabilities from Data

Cited by in corpus (12)

• Residual Dynamic Mode Decomposition: Robust and verified Koopmanism
• Data-driven modal decomposition methods as feature detection techniques for flow problems: a critical assessment
• Kernel Learning for Robust Dynamic Mode Decomposition: Linear and Nonlinear Disambiguation Optimization (LANDO)
• Structured Time-Delay Models for Dynamical Systems with Connections to Frenet-Serret Frame
• The Linear-Time-Invariance Notion of the Koopman Analysis-Part 2: Physical Interpretations of Invariant Koopman Modes and Phenomenological Revelations
• Adjoint-based phase reduction analysis of incompressible periodic flows
• Promoting global stability in data-driven models of quadratic nonlinear dynamics
• Mean resolvent operator of statistically steady flows
• LES-informed resolvent-based estimation of turbulent pipe flow
• Resolvent4py: a parallel Python package for analysis, model reduction and control of large-scale linear systems
• Capturing multiscale interactions in fluid flow via Lagrangian coherent structures and modal analysis
• Data-Driven Transient Growth Analysis