Bulletin of the American Physical Society
77th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 24–26, 2024; Salt Lake City, Utah
Session X12: Low-Order Modeling and Machine Learning in Fluid Dynamics: Methods VI |
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Chair: Fotis Sotiropoulos, Virginia Commonwealth University Room: 155 B |
Tuesday, November 26, 2024 8:00AM - 8:13AM |
X12.00001: Hybrid Auto-Encoder with SVD-like Convergence Nithin Somasekharan, Shaowu Pan Computational fluid dynamics involves solving large dynamical systems with millions of degrees of freedom, resulting in significant computational overhead. Linear dimensionality reduction techniques like Proper Orthogonal Decomposition (POD) are often used to create efficient representations of large-scale systems, aiding in predicting their temporal dynamics when integrated with a dynamic model in reduced space. Recent deep learning advances, such as autoencoders (AE), capture intrinsic nonlinear features for better compression and retrieval of high-fidelity information, outperforming POD at low ranks but struggling to provide rapid error convergence at higher ranks. This study aims to combine POD's linearity with AE's nonlinear feature extraction to achieve superior accuracy, robustness and convergence. Unlike hybrid approaches that simply combine POD and AE, our method introduces a learnable weighting parameter to balance contributions from both techniques, resulting in an adaptive weighted hybrid approach. We demonstrate the efficacy of this hybrid approach on various PDE datasets in fluid dynamics, including 1D Viscous Burgers, 1D Kuramoto-Sivashinsky, and 2D/3D Forced Isotropic Turbulence, achieving significant accuracy improvements over the aforementioned individual methods and reducing errors to machine precision at higher ranks. This work paves the way for high-quality reduced-order models, where model accuracy depends on efficient data compression and retrieval. |
Tuesday, November 26, 2024 8:13AM - 8:26AM |
X12.00002: Reduced Representations of Turbulent Rayleigh-Bénard Flows via Autoencoders Melisa Y Vinograd, Melisa Y Vinograd, Patricio Clark Di Leoni We analyzed the performance of Convolutional Autoencoders in generating reduced-order representations of Rayleigh-Bénard flows, with the aim of finding the smallest possible representations that still captures all relevant physics in the flow. We found that while at low Rayleigh numbers there is a clear minimum number of dimensions needed to compress up to the dissipation scale, at higher Rayleigh numbers the different, physics-based, metrics saturate at two different dimensions. At the lower dimension the autoencoder is able to represent up to mid-range scales and correctly estimate magnitudes such as the Nusselt number and the length of the boundary layer. At the higher dimension the autoencoders can represent up to the dissipation scale. We compare our architecture with two regularized variants as well as with linear methods. This study sets a path on how to proceed in finding the smallest possible representations of more and more turbulent flows. |
Tuesday, November 26, 2024 8:26AM - 8:39AM |
X12.00003: Data-driven linear analysis of turbulent flows via nonlinearity-subtracted dynamic mode decomposition Benjamin Herrmann, Katherine Cao, Carlos A Gonzalez, Steven L Brunton, Beverley J McKeon Mean-flow-based linear analyses of turbulent flows, such as resolvent analysis, provide valuable insight about flow structures and their dynamics that has been widely leveraged to model, control, and understand the underlying flow physics. However, these analyses are computationally expensive for flows over complex geometries and require the use of specialized codes that are typically only available in research environments. On the other hand, data-driven modal decompositions, such as the dynamic mode decomposition (DMD), identify turbulent flow structures that, although statistically relevant, do not provide insight into the physical mechanisms driving their dynamics. Here we introduce a novel data-driven method — nonlinearity-subtracted DMD (NSDMD) — that leverages knowledge of the structure of the Navier–Stokes equations to ensure that the learned operator is a low-rank approximation of the underlying mean-flow-linearized dynamics. Specifically, the method uses snapshots of the nonlinear terms in the perturbation equations to explicitly account for the contribution of the nonlinear forcing to the dynamics. We demonstrate the use of NSDMD to perform data-driven resolvent analysis on DNS and LES datasets, starting with a minimal channel flow and scaling up to the flow over a full aircraft model. As a result, NSDMD allows performing linear analyses of turbulent flows as a post-processing step on simulation data obtained with any available high-fidelity CFD code. |
Tuesday, November 26, 2024 8:39AM - 8:52AM |
X12.00004: Dynamic mode decomposition for self-similar dynamics Kevin Chen, Jacob Page Dynamic mode decomposition (DMD) has had enormous excess as a post-processing tool for both linear and nonlinear dynamical systems, where the output can in some circumstances be connected to a Koopman decomposition. Here, we explore the utility of Koopman and DMD in systems which collapse onto a self-similar solution. These dynamics are usually algebraic in time and it has been unclear how one might use DMD to identify the long-time, self-similar solution given early-time observations, or to estimate a collapse time onto such a solution. We demonstrate that both of these objectives can be accomplished by performing DMD on snapshots spaced equally in logarithmic time, and we will introduce several `rules of thumb’ for robust results. Our numerical experiments are supported by full analytical Koopman decompositions of the self-similar dynamical system for (1) a linear diffusion and (2) Burgers equation on the real line. Time permitting, we will also present some applications to two-dimensional vortex dynamics.
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Tuesday, November 26, 2024 8:52AM - 9:05AM |
X12.00005: A meshless method to compute the POD and its variants from scattered data Iacopo Tirelli, Miguel A Mendez, Andrea Ianiro, Stefano Discetti The Proper Orthogonal Decomposition (POD) is a widely adopted method for identifying patterns in fluid mechanics data. When data is organized on a fixed structured grid, such as in cross-correlation-based particle image velocimetry or in numerical simulations, POD is essentially equivalent to performing a cell-weighted Singular Value Decomposition (SVD) on the snapshot matrix. However, when data sampling locations change over time, as with mobile monitoring stations in meteorology and oceanography or with particle tracking velocimetry, interpolation is required to project the data onto a fixed grid before factorization. This interpolation is often both expensive and inaccurate. |
Tuesday, November 26, 2024 9:05AM - 9:18AM |
X12.00006: Non-Gaussian Variational Data Assimilation Embedded Reduced-Order Modeling Methods Through Statistical Error Transformations Muhammad Waleed Khan, Cheng Huang Predictions made by current simulation methods exhibit deficiencies in predicting high-speed reactive flows featuring nonlinear physics, such as turbulence and shocks, due to uncertainties in flow rates (e.g., boundary and initial conditions) or model assumptions. Data assimilation (DA) offers a potential solution to address such deficiencies by combining the numerical model of a system with real observations to find the most likely state. Most DA methods predominantly assume Gaussian distributions for system errors, whereas high-speed reactive flow features physics exhibiting non-Gaussian errors. Direct application of Gaussian-based DA methods are likely to produce biased or even non-physical predictions. This work presents a non-Gaussian variational DA method utilizing a transfer function to transform model predictions and observations into a Gaussian space, along with explicit representations of arbitrary error distributions which can be used for variational DA to maximize the posteriori. We evaluate and compare this new DA method with the standard ensemble Kalman filter (EnKF), four-dimensional variational (4DVar), and a normal-score EnKF and 4DVar approaches for reduced-order model (ROM) development. We use a suite of 1D test problems with prescribed strongly non-Gaussian system error distributions to perform the evaluations. The results show that the new non-gaussian Gaussian method produces more accurate state predictions than the standard Gaussian DA methods. |
Tuesday, November 26, 2024 9:18AM - 9:31AM |
X12.00007: Data-driven insights into fluid-structure association and energy quantification Cruz Y. Li, Yunlong Wang, Shuang Wu, Xisheng Lin, Tim K.T. Tse The linear-time-invariance notion to the Koopman Analysis (Part I - Li et al., 2022, Phys. Fluids 34(12) 125136; Part II - Li et al., 2023, J. Fluid Mech. 959, A15) and its derived augmented algorithm (Fu et al., 2023, Phys. Fluids 35(2) 025112) are recent advances in fluid mechanics, addressing the challenge of correlating nonlinear excitation and response in fluid-structure interactions (FSI). Continuing the serial research, this work presents a data-driven, Koopman-inspired approach integrated with the "Proper Orthogonal Decomposition-Dynamic Mode Decomposition-Discrete Fourier Transform Augmented Analysis (POD-DMD-DFT)" to decouple nonlinear FSI. This innovative approach first isolates energy-wise and evolution-wise significant nonlinear flow features, subsequently establishing cause-and-effect correspondences between these flow features and structure surface pressure. Dynamic visualizations of in-sync fluid-structure-coupled Koopman modes is then implemented for phenomenological analysis. Finally, FSI energy transfers is statistically quantified via spatiotemporal contribution and probability density distributions. Demonstrated based on high-fidelity direct numerical simulation and large eddy simulation of flow over typical rigid obstacles, our method offers insightful descriptions and interpretations of phenomena occurring in the flow and on the boundary (walls) of an FSI domain, and readily applies to various engineering problems given its data-driven nature. |
Tuesday, November 26, 2024 9:31AM - 9:44AM |
X12.00008: Flow dynamics from flow field measurements and a Galerkin Model. Qihong Lorena L Li Hu, Patricia García-Caspueñas, Andrea Ianiro, Stefano Discetti A novel methodology is proposed to improve the temporal resolution of non-time-resolved PIV measurements, allowing a better understanding of the dynamics of turbulent flows. In most cases, due to technological limitations such as maximum acquisition frequency or limited light source intensity, among others, time-resolved PIV can only be performed for specific cases where the maximum flow velocity is limited to low to moderate Reynolds number. |
Tuesday, November 26, 2024 9:44AM - 9:57AM |
X12.00009: A novel LES-augmented machine learning algorithm for turbulent flow and bed morphodynamics prediction in large-scale environments Zexia Zhang, Fotis Sotiropoulos, Ali Khosronejad In erodible channel environments, changes in bed topography can lead to the structural failure of device support structures and the spread of scour or deposition features within the channel. Thus, assessing sediment transport in large-scale waterways is a crucial environmental concern. However, high-fidelity simulations of bed evolution in large-scale rivers could be computationally expensive due to the costly two-way coupling between fluid dynamics and bed morphodynamics. We propose a novel convolutional neural network autoencoder (CNNAE) algorithm to predict the time-averaged shear stress distribution and equilibrium bed topography of mobile riverbeds in large-scale meandering rivers. The proposed method is highly efficient compared to high-fidelity simulations, requiring less than two percent of the computational cost to produce high-fidelity results. This study highlights the potential of the proposed machine-learning algorithm to reduce the computational costs of coupled hydro- and morpho-dynamics modeling in large-scale rivers. |
Tuesday, November 26, 2024 9:57AM - 10:10AM |
X12.00010: ABSTRACT WITHDRAWN
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