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 R15: Low-Order Modeling and Machine Learning in Fluid Dynamics: Methods IV |
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Chair: Jinlong Wu, University of Wisconsin - Madison Room: 155 E |
Monday, November 25, 2024 1:50PM - 2:03PM |
R15.00001: A transformer-based model for grid-agnostic full-field reconstruction of tsunami waves from sparse observations. Edward McDugald, Arvind T Mohan, Darren Engwirda, Javier Santos, Agnese Marcato The Senseiver (Santos et al., 2023) is a recently developed deep learning architecture based on the Perceiver-IO that facilitates sparse sensing and reconstruction of large, highly complex fields residing on arbitrary grids. This talk will discuss a recent implementation tailored to reconstruct tsunami waves from sparse measurements. We demonstrate the first successful ML-based full-field reconstructions of tsunami waves from sparse data based on physically realistic simulations with accurate bathymetry of the Pacific Ocean. We will provide an overview of the model architecture and our adjustments to facilitate its use for dynamics governed by shallow water equations. Our results consist of high-resolution, full-field tsunami wave reconstructions given incredibly sparse measurements corresponding to locations of ocean buoys currently deployed in the Pacific. Since our approach is domain agnostic, we aim to frame the method and results within the larger context of optimal sensor placement and data assimilation problems in fluid dynamics. We demonstrate significant advantages of the Senseiver, such as the ability to efficiently handle large domain sizes without the quadratic scaling complexity that impedes the practical use of transformers in earth sciences. |
Monday, November 25, 2024 2:03PM - 2:16PM |
R15.00002: Deep Reduced-Order Modeling for Fluids: The Importance of Autoencoder Initialization and Initial Transient Data Gregory Robert Macchio, Clarence W Rowley Many fluids systems may be approximated by dynamics on an inertial manifold, and we wish to obtain these dynamics from data by training a collection of neural networks. In particular, we train an autoencoder to learn the invariant manifold, and learn the dynamics separately, either by training a separate neural network, or a polynomial approximation. Many previous studies limit training data to consider only points that have already relaxed onto the inertial manifold, and neglect the ``transient.'' We find that including the transients can be important, especially for learning projections of initial conditions that are even slightly off the inertial manifold. Furthermore, we find that training time is dramatically decreased if the autoencoder is structured to explicitly include a linear approximation of the inertial manifold. As examples, we construct two-dimensional and eight-dimensional reduced-order models for the complex Ginzburg-Landau equation in its supercritical regime and the Kuramoto-Sivashinsky equation in its chaotic regime, respectively. |
Monday, November 25, 2024 2:16PM - 2:29PM |
R15.00003: Feature-Guided Adaptive Model Order Reduction for Convection-Dominated Problems Ali Mohaghegh, Cheng Huang Physical problems featuring strong convections (e.g., hypersonic flows and detonations) often present significant challenges and are well-recognized to be not amendable for conventional model-order reduction (MOR) methods. This can be mainly attributed to the well-known issues associated with the slow decay of Kolmogorov N-width. In literature, several remedies have been proposed to address this challenge via local subspaces, nonlinear manifolds, or adaptive MOR. In this work, we focus on formulating a feature-guided adaptive projection-based model order reduction (MOR) method to develop reduced-order model (ROM) for convection-dominated problems involving flames and shocks, which dynamically update the subspace during online execution to optimally capturing the crucial dynamics. Such adaptive ROM requires minimal offline training and inherently supports predictions of future states and parametric variations. To maximize efficiency and effectiveness, we develop a feature-guided sampling strategy that strategically populates sampling points to capture the prominent convective features with rigorous error controls, ensuring accurate prediction of the advection dynamics. A suite of challenging convection-dominated testing problems is used to assess the feature-guided sampling strategy, which includes sod shock tube, colliding shock waves, and detonation waves. |
Monday, November 25, 2024 2:29PM - 2:42PM |
R15.00004: Linear and nonlinear Granger causality analysis of turbulent flows Barbara Lopez-Doriga, Marco Atzori, Ricardo Vinuesa, H. Jane Bae, Ankit Srivastava, Scott T. M. Dawson This work presents a novel nonlinear extension of multivariate Granger causality analysis to enable the study of second-order (and if needed, higher-order) nonlinear interactions between energetically-dominant coherent structures in turbulent flows. We focus in particular on turbulent flow through a square duct, which features a secondary mean flow containing pairs of counter-rotating streamwise vortices located near the duct corners (Prandtl's secondary flow of the second kind). This secondary mean flow has velocities significantly smaller in magnitude than the streamwise mean flow component. We apply the proposed causality analysis framework upon temporal coefficients of proper orthogonal decomposition modes, which are obtained from direct numerical simulation data. The analysis suggests that secondary flow fluctuations are the principal driver for both the formation of the near-wall and near-corner streamwise streaks, and for the motion of these structures towards and away from the corner. We further distinguish between linear and nonlinear causal mechanisms present in the system. |
Monday, November 25, 2024 2:42PM - 2:55PM |
R15.00005: Extracting self-similarity from data Nikolaos Bempedelis, Luca Magri, Konstantinos Steiros The identification of self-similarity is an indispensable tool for understanding and modelling a wide variety of fluid mechanical phenomena. Unfortunately, this is not always possible to perform formally in highly complex problems. We propose a methodology to extract the similarity variables of a self-similar physical process directly from data, without prior knowledge of the governing equations or boundary conditions, based on an optimization problem and symbolic regression. We analyze the accuracy and robustness of our method in four problems which have been influential in fluid mechanics research: a laminar boundary layer, Burger’s equation, a turbulent wake, and a collapsing cavity. Our analysis considers datasets acquired via both numerical and wind-tunnel experiments. |
Monday, November 25, 2024 2:55PM - 3:08PM |
R15.00006: Neural Inference of Fluid–Structure Interactions from Lagrangian Particle Tracks Rui Tang, Ke Zhou, Samuel J Grauer, jifu tan Fluid–structure interactions (FSI) involve flexible structures that couple to internal or external flow. We report a novel configuration of physics-informed neural networks (PINNs) to reconstruct FSI from a sparse set of Lagrangian particle trajectories, called tracks. To do this, we use a "fluid network" to represent the liquid or gas phase; a "solid network" models the surface response via coefficients of a parameterized surface. Data are included in the algorithm via a "kinematics-constrained track" model that embeds the advection equation as a hard constraint and can handle noise and inertial transport effects. We specify data and physics losses for the fluid, as well as a no-slip boundary loss for inter-phase coupling. Minimizing the aggregate loss yields spatiotemporally resolved flow states that are consistent with observed data and governing equations for the fluid and a surface response that complies with the boundary condition. Crucially, the approach does not require a constitutive model for the solid phase. We demonstrate our method synthetically using 2D flow over a flapping plate and 3D flow inside a flexible pipe. Accurate reconstructions of both phases are obtained from the sparse, noisy tracks. |
Monday, November 25, 2024 3:08PM - 3:21PM |
R15.00007: Physics-Constrained Forecasting of Fluid Dynamics with Reservoir Computing Dima Tretiak, Anastasia Bizyaeva, Nathan Kutz, Steve Brunton We present a new approach for incorporating physical constraints into Reservoir Computers (RCs). The long-term aim of this work is to increase the interpretability of RCs while mitigating the computational costs associated with training RCs for high dimensional problems, such as spatiotemporal fluid flows. A Reservoir Computer is, itself, a dynamical system, commonly implemented as a single-layer recurrent neural network in which only the linear output layer is trained and all other parameters are randomly initialized and fixed. Therefore, training an RC only involves solving a least squares problem which—while interpretable and efficient for small problems—scales poorly for problems of higher dimension. Due in part to this limitation, RCs have seldom been applied to spatial fluid flows despite significant interest in doing so. We show that physical constraints such as conservation laws and boundary conditions can be imposed in the training procedure and can be guaranteed to hold for forecasting. To enforce the constraints, we modify the RC training procedure with a linear homogeneous constraint represented by a differentiation matrix. We demonstrate the efficacy of this method by imposing zero-divergence and periodic boundary condition constraints for 2D incompressible fluid flow. |
Monday, November 25, 2024 3:21PM - 3:34PM |
R15.00008: Combined autoencoder and clustering-based approach to investigate extreme events in turbulent flows Nguyen Anh Khoa Doan, Luca Magri Turbulent flows may exhibit extreme events, which are sudden large amplitude changes of the flow state. The physical understanding and prediction of extreme events are intricate due to chaos, high dimensionality, and the (relatively) infrequent occurrence of the events. |
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