Sparse identification of nonlinear dynamics with low-dimensionalized flow representations

Abstract

We perform a sparse identification of nonlinear dynamics (SINDy) for low-dimensionalized complex flow phenomena. We first apply the SINDy with two regression methods, the thresholded least square algorithm (TLSA) and the adaptive Lasso (Alasso) which show reasonable ability with a wide range of sparsity constant in our preliminary tests, to a two-dimensional single cylinder wake at $R{e}_D=100$, its transient process, and a wake of two-parallel cylinders, as examples of high-dimensional fluid data. To handle these high dimensional data with SINDy whose library matrix is suitable for low-dimensional variable combinations, a convolutional neural network-based autoencoder (CNN-AE) is utilized. The CNN-AE is employed to map a high-dimensional dynamics into a low-dimensional latent space. The SINDy then seeks a governing equation of the mapped low-dimensional latent vector. Temporal evolution of high-dimensional dynamics can be provided by combining the predicted latent vector by SINDy with the CNN decoder which can remap the low-dimensional latent vector to the original dimension. The SINDy can provide a stable solution as the governing equation of the latent dynamics and the CNN-SINDy based modeling can reproduce high-dimensional flow fields successfully, although more terms are required to represent the transient flow and the two-parallel cylinder wake than the periodic shedding. A nine-equation turbulent shear flow model is finally considered to examine the applicability of SINDy to turbulence, although without using CNN-AE. The present results suggest that the proposed scheme with an appropriate parameter choice enables us to analyze high-dimensional nonlinear dynamics with interpretable low-dimensional manifolds.

References in corpus (28)

• Discovering governing equations from data: Sparse identification of nonlinear dynamical systems
• Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis
• Data-driven discovery of coordinates and governing equations
• Super-resolution reconstruction of turbulent flows with machine learning
• Sparse identification of nonlinear dynamics for model predictive control in the low-data limit
• Nonlinear mode decomposition with convolutional neural networks for fluid dynamics
• Machine learning based spatio-temporal super resolution reconstruction of turbulent flows
• Perspectives on Machine Learning-augmented Reynolds-averaged and Large Eddy Simulation Models of Turbulence
• Discovery of Algebraic Reynolds-Stress Models Using Sparse Symbolic Regression
• Global field reconstruction from sparse sensors with Voronoi tessellation-assisted deep learning
• Sparse reduced-order modeling : Sensor-based dynamics to full-state estimation
• Assessment of supervised machine learning methods for fluid flows
• Convolutional neural network and long short-term memory based reduced order surrogate for minimal turbulent channel flow
• Convolutional neural network based hierarchical autoencoder for nonlinear mode decomposition of fluid field data
• Machine-learning-based reduced order modeling for unsteady flows around bluff bodies of various shapes
• Multi-level Convolutional Autoencoder Networks for Parametric Prediction of Spatio-temporal Dynamics
• Discovery of Nonlinear Multiscale Systems: Sampling Strategies and Embeddings
• Probabilistic neural networks for fluid flow surrogate modeling and data recovery
• Synthetic turbulent inflow generator using machine learning
• Convolutional neural networks for fluid flow analysis: toward effective metamodeling and low-dimensionalization
• Assessment of unsteady flow predictions using hybrid deep learning based reduced order models
• Experimental velocity data estimation for imperfect particle images using machine learning
• Formulating turbulence closures using sparse regression with embedded form invariance
• Generalization techniques of neural networks for fluid flow estimation
• SPOD and resolvent analysis of near-wall coherent structures in turbulent pipe flows
• Low-order model for successive bifurcations of the fluidic pinball
• Recovering missing CFD data for high-order discretizations using deep neural networks and dynamics learning
• Prediction of wall-bounded turbulence from wall quantities using convolutional neural networks

Cited by in corpus (24)

• Convolutional neural network and long short-term memory based reduced order surrogate for minimal turbulent channel flow
• Super-Resolution Analysis via Machine Learning: A Survey for Fluid Flows
• Convolutional neural networks for fluid flow analysis: toward effective metamodeling and low-dimensionalization
• Experimental velocity data estimation for imperfect particle images using machine learning
• Generalization techniques of neural networks for fluid flow estimation
• Reduced order modeling of parametrized systems through autoencoders and SINDy approach: continuation of periodic solutions
• Nonlinear proper orthogonal decomposition for convection-dominated flows
• Assessments of epistemic uncertainty using Gaussian stochastic weight averaging for fluid-flow regression
• Data-driven transient lift attenuation for extreme vortex gust-airfoil interactions
• Data-driven nonlinear turbulent flow scaling with Buckingham Pi variables
• A Framework Based on Symbolic Regression Coupled with eXtended Physics-Informed Neural Networks for Gray-Box Learning of Equations of Motion from Data
• Discovery of partial differential equations from highly noisy and sparse data with physics-informed information criterion
• Compressing fluid flows with nonlinear machine learning: mode decomposition, latent modeling, and flow control
• Robust training approach of neural networks for fluid flow state estimations
• Dynamical system prediction from sparse observations using deep neural networks with Voronoi tessellation and physics constraint
• Reconstructing three-dimensional bluff body wake from sectional flow fields with convolutional neural networks
• Rheo-SINDy: Finding a Constitutive Model from Rheological Data for Complex Fluids Using Sparse Identification for Nonlinear Dynamics
• Data-driven Discovery of Delay Differential Equations with Discrete Delays
• Flow control by a hybrid use of machine learning and control theory
• Data-assisted, physics-informed propagators for recurrent flows
• Compact representation of transonic airfoil buffet flows with observable-augmented machine learning
• Model order reduction with neural networks: Application to laminar and turbulent flows
• Banach neural operator for Navier-Stokes equations
• Sparse Identification for bifurcating phenomena in Computational Fluid Dynamics