Bulletin of the American Physical Society
75th Annual Meeting of the Division of Fluid Dynamics
Volume 67, Number 19
Sunday–Tuesday, November 20–22, 2022; Indiana Convention Center, Indianapolis, Indiana.
Session Z21: Nonlinear Dynamics: Data-Driven |
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Chair: Rambod Mojgani, Rice University; Nguyen Anh Khoa Doan, Delft University of Technology Room: 207 |
Tuesday, November 22, 2022 12:50PM - 1:03PM |
Z21.00001: Why are the data-driven surrogates of multi-scale dynamical systems long-term unstable? Ashesh K Chattopadhyay, Ebrahim Nabizadeh, Pedram Hassanzadeh |
Tuesday, November 22, 2022 1:03PM - 1:16PM |
Z21.00002: Calibration of projection-based compressible flow reduced order models with quadratic manifold approximation Victor Zucatti Reduced order modeling is a popular approach that generates surrogate models by combining physics-based or data-driven techniques with a lower dimensional representation from training generated data. Linear reduction approximations such as proper orthogonal decomposition (POD) are commonly used in model order reduction. However, complex flow problems could require hundreds, if not thousands, of modes to produce an accurate reduced order model (ROM). Recently, nonlinear techniques have emerged as a solution to this shortcoming. In principle, nonlinear methods allow for a much smaller basis. Unfortunately, most nonlinear methods usually come with issues that undermine their viability to large scale problems. In this work, a quadratic manifold approach is implemented and analyzed to solved unsteady compressible flow problems. In particular, this techniques allows for pre-computation of the ROM coefficients when a non-conservative compressible Navier-Stokes equation formulation is used. Moreover, a data-driven calibration of the ROM is applied to enhance accuracy and stability. |
Tuesday, November 22, 2022 1:16PM - 1:29PM Not Participating |
Z21.00003: Modeling low-frequency dynamics in turbulent flows using data Sijie Huang, Jeonglae Kim In turbulent flows, events correlated over a long time period are observed occasionally. Some of those events take place on a regular basis, but they tend to occur without apparent periodicity or even intermittently. They are manifested usually by a low-frequency oscillation of characteristic variables. Such dynamics is often associated with an abrupt increase (or decrease) of friction drag, mixing, heat transfer, and aerodynamic noise, thus affecting the stability and robustness of flow systems. Describing and predicting such events are not straightforward and dependent on heuristic and statistical approaches, lacking direct connection with the first principle from which they originate. This study combines a data-driven algorithm and a short-time averaging to systematically educe a partial differential equation (PDE) model optimally describing the low-frequency dynamics. The proposed formulation is tested for linear advection--diffusion equation, complex Ginzburg--Landau equation, and Navier--Stokes equations. Upon choosing an appropriate averaging time scale, the effects of fast dynamics are suppressed by the short-time averaging, making a PDE model for slow dynamics more amenable to be discovered at a significantly lower computational cost. |
Tuesday, November 22, 2022 1:29PM - 1:42PM |
Z21.00004: Data-driven discovery and extrapolation of parameterized pattern-forming dynamics Zachary G Nicolaou, Steven L Brunton, J. Nathan Kutz, Guanyu Huo, Yihui Chen We develop a data-driven approach SINDyCP to discover dynamics for systems with adjustable control parameters, such as an external driving strength. We demonstrate the method on systems of varying complexity, ranging from discrete maps to systems of partial differential equations. To mitigate the impact of measurement noise, we also develop a weak formulation of SINDyCP and assess it's performance on noisy data. Applications include the discovery of universal pattern-formation equations from experimental data and extrapolation beyond the weakly nonlinear regime near the onset of an instability. |
Tuesday, November 22, 2022 1:42PM - 1:55PM |
Z21.00005: Data-driven prediction of Jacobians and Covariant Lyapunov Vectors in chaotic flows Georgios Margazoglou, Luca Magri In a chaotic flow, infinitesimal perturbations grow exponentially in time. Their evolution is governed by the tangent dynamics, which, in turn, is governed by the Jacobian. From the Jacobian, the perturbations' growth rates (Lyapunov exponents, LEs), and directions (covariant Lyapunov vectors, CLVs) can be computed, which are key to computing the stability and the gradient for design optimization. The derivation and numerical solution of the tangent equation and its adjoint, however, may be time consuming and cumbersome. To overcome this, we propose a method to infer the tangent dynamics from data. We develop and train Echo State Networks (ESNs) on data of prototypical chaotic dynamical systems. We compute the Networks' Jacobian, from which we extract its spectrum of LEs, and CLVs. We find that (i) the long-term statistics, and (ii) the finite time variations in physical space of both LEs and CLVs agree with the target sets. Hence, we show that (iii) ESNs are able to accurately learn the stability properties of chaotic attractors. This work opens opportunities to physically interpret the stability and compute the gradient of chaotic and turbulent flows from experimental data. |
Tuesday, November 22, 2022 1:55PM - 2:08PM |
Z21.00006: Constructing invariant solutions of wall-bounded shear flows by a Jacobian-free adjoint-based method Omid Ashtari, Tobias M Schneider The dynamics of fluid turbulence is underpinned by invariant solutions embedded in the state space of the governing equations. Finding an invariant solution of a certain type can be viewed as an optimization problem over space-time fields with prescribed temporal behavior: minimizing a cost function that penalizes the deviation of space-time fields from being a solution to the governing equations. We propose a Jacobian-free algorithm based on an adjoint-based minimization technique for constructing invariant solutions of wall-bounded shear flows. We demonstrate the feasibility of the algorithm by applying it to plane Couette and plane Poiseuille flows. Unlike the state-of-the-art Newton-based alternatives, this approach is robust to inaccurate initial guesses, and is not affected by the exponential separation of trajectories. We also propose a data-driven procedure for accelerating the convergence of the adjoint-descent algorithm. |
Tuesday, November 22, 2022 2:08PM - 2:21PM |
Z21.00007: Discovery of interpretable structural model errors by combining Bayesian sparse regression and data-assimilation Rambod Mojgani, Ashesh K Chattopadhyay, Pedram Hassanzadeh Loss in accuracy of models originates from inaccuracies of |
Tuesday, November 22, 2022 2:21PM - 2:34PM |
Z21.00008: Optimal Sparse Sensor Placement with Adaptive Constraints for Nuclear Digital Twins Niharika Karnik, Mohammad G Abdo, Krithika Manohar Nuclear applications lack the luxury of immersing the physical asset with a large number of sensors due to cost constraints, harsh conditions and physical inaccessibility. Thus, optimal sensor placement with spatial constraints is an important design consideration to enable flow field reconstruction and digital twinning of nuclear assets. Design considerations may include preset sensor locations, blocked regions of a reactor, or a fixed number of sensors within a user-specified region or a user-specified distance from other sensors. The developed algorithm handles optimal sensor placement by incorporating these spatial constraints into a well-established greedy algorithm for the optimal sensor placement problem. It is capable of providing sensor locations on a grid based on user-defined constraints and can be expanded to various applications such as climate science and fluid dynamics. In this work the algorithm is demonstrated on the Opti-TWIST (Transient Water Irradiation System) prototype which is electrically heated to mimic the neutronics effect and will be inserted into the Transient Reactor Test facility (TREAT) at Idaho National Laboratory (INL). |
Tuesday, November 22, 2022 2:34PM - 2:47PM |
Z21.00009: Trajectory-optimized cluster-based network model for the three-dimensional sphere wake Chang Hou, Nan DENG, Bernd R Noack We propose a fully automatable data-driven method to model unsteady flow dynamics, namely the trajectory-optimized Cluster-based Network Model (tCNM). Stating with CNM [1,2], the snapshot trajectories are tracked with improved accuracy by tCNM, where centroids are shifted to obtain a more accurate representation, and supporting points are added to get a refined state propagation. Three-dimensional sphere wakes are used to validate tCNM, including periodic shedding, quasi-periodic shedding and chaotic shedding. The representation error is five times smaller compared to the closest centroid approximation. This improvement indicates that tCNM can achieve the same accuracy as Proper Orthogonal Decomposition (POD) of the same order, while retaining the advantage of high physical interpretability. tCNM and other extensions of cluster-based modeling [3,4] constitute a promising alternative to POD methods, which can be applied to numerous other applications and extended to parametric and control-oriented reduced-order models. |
Tuesday, November 22, 2022 2:47PM - 3:00PM |
Z21.00010: Dynamics-based machine learning of transitions in shear flows Balint Kaszas, Mattia Cenedese, George Haller Several approaches have been proposed to deriving reduced-order models for exact coherent states (ECSs) and transitions among them in canonical shear flows, such as the plane Couette flow. One such approach uses truncated modal projections of the Navier-Stokes equations. This technique may lead to reasonably accurate models but fails to provide a priori estimates for the necessary number of modes to be included and the magnitude of the truncation error. Alternative approaches include the Dynamic Mode Decomposition (DMD and Koopman decomposition, which fit linear dynamical systems to a set of observables. By their linearity, however, these approaches cannot produce reduced models that capture fundamentally nonlinear phenomena, such as coexisting ECSs and transitions among them. |
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