Bulletin of the American Physical Society
72nd Annual Meeting of the APS Division of Fluid Dynamics
Volume 64, Number 13
Saturday–Tuesday, November 23–26, 2019; Seattle, Washington
Session P10: Nonlinear Dynamics: Model Reduction III |
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Chair: Benjamin Herrmann, University of Washington Room: 3A |
Monday, November 25, 2019 5:16PM - 5:29PM |
P10.00001: Time-frequency analysis of intermittent coherent structures in turbulent flows Aaron Towne, Peijing Liu Time-frequency analysis is a popular and powerful tool for identifying and analyzing intermittent events in fluid systems. Typically, these analyses are carried out by computing spectrograms or scalograms from the time history of a single flow variable at a single location in space, e.g., one component of velocity at some location of interest. A disadvantage of this approach is that the relationship between spectrograms or scalograms computed at different points in the flow or for different flow quantities is ambiguous, and, in particular, the role of coherent structures in producing the observed intermittency is obscured. In this presentation, we introduce an approach for generating global spectrograms and scalograms that describe the time-frequency behavior of coherent structures defined over all flow variables and spatial locations. The method is based on two extensions of spectral proper orthogonal decomposition, which defines flow structures that evolve coherently in space and time (Towne et al., J. Fluid Mech. Vol. 847, 2018). We demonstrate the method using the example of coherent wavepacket structures in a turbulent jet. [Preview Abstract] |
Monday, November 25, 2019 5:29PM - 5:42PM |
P10.00002: A modal decomposition for discovery of nonlinear triadic interactions from flow data Oliver Schmidt We seek a decomposition of a flow field into spatial modes that reveal the footprint of triadic interactions. This goal is accomplished by extending bispectral signal analysis to multidimensional datasets with at least one inhomogeneous spatial direction. As we are interested in finding the dominant large-scale coherent structures associated with quadratic nonlinearities, we require the modal decomposition to optimally represent the data in terms of its phase coherence, as characterized by the third-order cumulant. In the frequency domain, this higher-order statistic is readily computed from a product of Fourier transforms at different frequencies. An algorithm for the computation of the proposed bispectral mode analysis is presented and applied to three data sets obtained from direct numerical simulation of cylinder flow at Re=300, large-eddy simulation of transitional jet flow, and particle image velocimetry measurements of a massively separated flat plate at a high angle of attack. The results are visualized in terms of frequency-frequency plots similar to the bispectrum that indicate the presence of the quadratic phase coupling, and spatial modes that can reveal the nature of the nonlinear interaction. [Preview Abstract] |
Monday, November 25, 2019 5:42PM - 5:55PM |
P10.00003: Real-Time Reduced Order Modeling Of Deterministic and Stochastic Systems Using Time-Dependent Low-Rank Basis Hessam Babaee, Michael Donello We present a scalable method for the extraction of a time-dependent basis from observations of deterministic/stochastic systems. This method is based on a variational principle whose optimality condition leads to a closed-form evolution equation of the basis. The method is scalable with respect to the size of the data and the reduction order. We will also present real-time reduced order model, which are constructed from projections of the full-dimensional dynamics onto the time-dependent basis. We will present two case studies for the reduced-order modeling of: (1) transient instabilities in Kuramoto-Sivashinsky equation, and (2) transient flow over a bump. [Preview Abstract] |
Monday, November 25, 2019 5:55PM - 6:08PM |
P10.00004: Data-driven modeling of chaotic flows with non-Gaussian statistics Hassan Arbabi, Themistoklis Sapsis We present a data-driven framework for modeling chaotic flows in the form of linear stochastic differential equations (SDEs) observed under a nonlinear map. We discover the nonlinear map using the theory of optimal transport for measures, and identify the system of SDEs by matching the spectral density of the optimally transported data. The inclusion of the nonlinear observation map allows us to build models of chaotic systems with moderate dimensions (e.g. 10 and more) that capture non-Gaussian features of the invariant measure including skewness and heavy tails. We demonstrate the application of our framework through a few examples including a high-Reynolds cavity flow and observational climate data. [Preview Abstract] |
Monday, November 25, 2019 6:08PM - 6:21PM |
P10.00005: Reduced order flow control using input-output hidden Markov model Palash Sashittal, Daniel Bodony In this work we extend the cluster based reduced order modeling framework to partially observed fluid systems with a control oriented perspective. We employ a data-driven model learning approach coupled with a closed-loop control strategy. Model parameters are learned using expectation maximization in the presence of scarce and noisy data. Two feedback controller design methods are proposed to control the long term behavior of the system. We demonstrate the performance of the controllers by controlling the transitions of the Lorenz system and to suppress the nonlinear vortex shedding past an inclined flat plate. The application of hidden Markov model based control to primary atomization of a liquid jet in a high-speed gas co-flow will be discussed. [Preview Abstract] |
Monday, November 25, 2019 6:21PM - 6:34PM |
P10.00006: Autoencoders for discovering coordinates and dynamics from data Kathleen Champion, Bethany Lusch, Nathan Kutz, Steven Brunton Understanding and efficiently modeling high-dimensional scientific data such as fluid flows require methods for identifying interpretable reduced models from the data. Deep learning methods are extremely flexible, showing a remarkable ability to behave as universal function approximators and demonstrating impressive performance at modeling and predictive tasks; however the resulting models have many parameters and are notoriously difficult to interpret. On the other hand, methods such as the sparse identification of nonlinear dynamics (SINDy) provide parsimonious interpretable models, but require knowledge of the proper coordinates for representing dynamics. In this work, we present a method that combines an autoencoder network with SINDy for the simultaneous discovery of reduced coordinates and parsimonious dynamical models from high-dimensional data. The resulting models are interpretable, containing a small number of active terms that describe the dynamics in the reduced space. We demonstrate the success of this approach on data from a number of example systems. [Preview Abstract] |
Monday, November 25, 2019 6:34PM - 6:47PM |
P10.00007: Identifying coarse-grained PDE models from data with the sparse identification of nonlinear dynamics Kadierdan Kaheman, Eurika Kaiser, Aditya Nair, Nathan Kutz, Steven Brunton Identifying reduced order models of complex systems, such as are found in fluid mechanics, is a challenging, yet vital topic. In addition to Galerkin projection, which has been a mainstay of the fluid mechanics' community for decades, techniques from machine learning are emerging to identify accurate and efficient models from data. The sparse identification of nonlinear dynamics (SINDy) algorithm has recently been shown to provide data-driven reduced-order models for fluids that are both interpretable and generalizable. However, it is difficult to identify models with rational function nonlinearities using the SINDy approach, although these dynamics appear in many systems of interest, especially those systems with a separation of timescales. A recent extension to SINDy has enabled the identification of rational function nonlinearities, but this approach is numerically fragile and highly sensitive to noise. In this work, we develop a robust extension of SINDy to identify rational function nonlinearities, using an iterative approach to improve the conditioning of the algorithm. We demonstrate this implicit SINDy approach on several ODE and PDE systems, including the unsteady BZ chemical flow reaction. [Preview Abstract] |
Monday, November 25, 2019 6:47PM - 7:00PM |
P10.00008: A study of state-of-the-art model reduction techniques applied to flow simulations with moving immersed boundaries Serena Costanzo, Taraneh Sayadi, Pascal Frey Reducing a detailed system into smaller sized models, capable of reproducing the main features and dynamics of the original configuration is a common practice in optimisation and control community, which could also serve as a way to make function evaluations less expensive. Since control is one of the future applications of this study it is necessary to identify the most suitable methodology applicable to detailed Navier-Stokes simulations for prediction purposes. To this end various strategies such as the GNAT method (Gauss-Newton with approximate tensors), POD with Galerkin regression method, implemented with the machine learning algorithm SINDy (Sparse Identification of Nonlinear Dynamics), and conventional POD-DEIM methods are compared in the context of an incompressible Navier-Stokes solver with immersed boundaries capabilities. The capability of these methods to interpolate between various operating conditions and to extrapolate the solution is investigated. The ability of each reduction strategy in dealing with existing nonlinearities and moving immersed boundaries is also identified. [Preview Abstract] |
Monday, November 25, 2019 7:00PM - 7:13PM |
P10.00009: Learning interpretable stochastic models with sparse regression Jared Callaham, Jean-Christophe Loiseau, J. Nathan Kutz, Steven Brunton Low-dimensional modeling is a promising avenue for enabling design, control, and physical understanding of complex flows. Data-driven approaches, which leverage the increasing availability of numerical and experimental data, are of particular interest. Recent results on laminar flows show that sparse Galerkin regression can be an effective tool for developing accurate minimum-complexity models. However, the separation of scales in turbulence presents a challenge for these fully resolved models. Alternatively, only dominant global variables may be explicitly modeled with smaller scales treated as stochastic forcing. When the dominant behavior is thought to be well-described by stereotypical dynamics such as the normal form of a bifurcation, the model parameters may be estimated using physical arguments or least-squares regression. More generally, we may not know the form of the equations a priori, and would like to discover a model directly from data. We describe an approach to learning interpretable stochastic models, devoting particular attention to practical considerations such as low sampling rates and time-correlated forcing. We apply our approach to prototypical nonlinear dynamics and demonstrate more accurate recovery than existing stochastic model discovery methods. [Preview Abstract] |
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