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 ZC12: Low-Order Modeling and Machine Learning in Fluid Dynamics: General IV |
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Chair: Theresa Saxton-Fox, University of Illinois at Urbana-Champaign Room: 155 B |
Tuesday, November 26, 2024 12:50PM - 1:03PM |
ZC12.00001: Input-Output Neural Operator model for Jet in Crossflow Federico Rios Tascon, Aakash Patil, Peter J Schmid, Beverley J McKeon A Fourier Neural Operator (FNO)-based network is used as an Input-output model to study Direct Numerical Simulation (DNS) jet-in-crossflow. The network consists of a non-linear encoder and decoder, and a single linear Fourier layer corresponding to the model's latent space, which allows us to obtain a linear mapping between input and output variables in an encoded space. This linear mapping is a powerful tool, enabling us to get an approximation of the Koopman operator, serve as a mapping between spatial regions of the flow, or map one state variable to another. For each case, an appropriate loss function and network setup is implemented. These mappings permit us to draw conclusions regarding the relative importance of sub-processes in a flow through input-output analysis. This network was originally developed and implemented using Large Eddy Simulation (LES) channel flow data, and now performing a coordinate transform of the jet-in-crossflow data into a frame that follows the center streamline of the jet, we analyze this flow in a similar manner. |
Tuesday, November 26, 2024 1:03PM - 1:16PM |
ZC12.00002: Fourier neural operators for classifying images with varying sizes in one shot training: Applied to 3D digital porous media Ali Kashefi, Tapan Mukerji Fourier Neural Operators (FNOs) are invariant to the size of input images, allowing them to process images of any size without altering the network architecture, unlike traditional convolutional neural networks (CNNs). Using this advantage of FNOs, we propose a novel deep learning framework designed for classifying images with varying sizes. In this approach, the proposed FNO-based framework is trained on images of multiple sizes simultaneously. As a practical application, we consider predicting permeability of three-dimensional digital porous media. From a computer science perspective, an intuitive approach to construct the desired FNO framework would be to connect the output of FNO layers to a classifier using adaptive max pooling. However, we demonstrate that while this intuitive approach works for porous media with fixed sizes, it fails for those with varying sizes. To overcome this challenge, we introduce our approach: instead of adaptive max pooling, we utilize static max pooling with the channel width of FNO layers. Because the channel width of FNO layers is independent of the input image size, our framework can accommodate images of varying sizes during training. We demonstrate the effectiveness of our proposed framework by comparing its performance with the intuitive approach using the example of classifying three-dimensional digital porous media of different sizes. |
Tuesday, November 26, 2024 1:16PM - 1:29PM |
ZC12.00003: Distributed Low-Dimensional Models for Predicting Large Spatiotemporally Chaotic Dynamical Systems Cristian Ricardo Constante Amores, Alec J Linot, Michael David Graham Fluid flows are characterized by a chaotic motion, a large number of degrees of freedom, and a multi-scale nature in both space and time. With the availability of large sets of data through image analysis and high-performance computing, research has focused on developing data-driven Reduced-Order Models (ROMs) to accurately capture flow dynamic. However, data-driven models face challenges when dealing with high dimensionality, unknown physics lows, and nonlinearity. These factors make it difficult to effectively model the underlying dynamics of those systems and extract meaningful insights from data. This study aims to use machine learning techniques to predict spatially large fluid dynamics highly chaotic systems. As the domain increases, ROMs become more challenging, resulting in the worsening of the model performance and the increase of computational feasibility. We propose a solution to this problem by considering localized spatial regions, `patches', as separate dynamical systems that are equivalent and communicate with one another. Here, we target the two-dimensional Kolmogorov flow, and we significantly reduce the high-dimensional nature of the state space, via autoencoders, and NODEs for the spatio-temporal forecasting of the latent space. This methodology, referred to as Distributed Data-driven Manifold Dynamics (DisDManD), provides the ability to capture accurately the system dynamics in terms of short-time tracking and long-time statistics. |
Tuesday, November 26, 2024 1:29PM - 1:42PM |
ZC12.00004: Relating Skewness and Fourier Harmonics in Low Reynolds Number Wake Flow Krithsanvith Manthripragada, Theresa A Saxton-Fox In the study of simple, laminar wake flows, it is observed that multiple Fourier modes are necessary to accurately describe the wake's dynamics, even though these flows exhibit perfect periodicity with a single period. The spatial configuration of these modes shows distinct patterns: odd harmonics exhibit a peak at the wake center, while even harmonics display a zero crossing at the same location. Our research reveals that these harmonic structures are intrinsically linked to the skewness present in the wake's vorticity field. By employing simple mathematical models and analyzing laminar wake flow data, we establish that data with non-zero skewness require multiple Fourier modes to represent the flow dynamics, even for signals that are perfectly periodic. Furthermore, we elucidate the mathematical relationship between the skewness of the vorticity field and the phases of the corresponding Fourier modes, demonstrating how these phase shifts influence the spatial distribution of the Fourier modes. This work provides new insights into the fundamental mechanisms governing wake flows and underscores the significance of skewness in fluid dynamics analysis. |
Tuesday, November 26, 2024 1:42PM - 1:55PM |
ZC12.00005: Abstract Withdrawn
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Tuesday, November 26, 2024 1:55PM - 2:08PM |
ZC12.00006: The role of basis functions in reduced-order modelling for plane Couette flow Zilin Zong, Irma Burazorovic, Igor Maia, André Cavalieri, Yongyun Hwang This study examines the effect of basis functions on reduced order models (ROMs) on capturing the flow physics of parallel shear flows, focusing on plane Couette flow at Re=500 within a minimal flow unit domain. Four different sets of POD-mode-based basis functions are computed from 1) DNS (POD-DNS); 2) stochastic response of the linearised Navier-Stokes (LNS) operator about the laminar base flow (POD-LB); 3) stochastic response of the LNS operator about turbulent mean flow (POD-TM); 4) stochastic response of an eddy-viscosity-enhanced LNS operator about turbulent mean flow (POD-ETM). The ROMs are subsequently constructed using Galerkin projections, and they all show converged flow statistics at sufficiently large degrees of freedom (DoF). When truncated moderately, both POD-DNS and POD-ETM show better performance than the other two cases especially for replicating turbulence statistics and dynamics. However, they do not retain the linear stability of the laminar state especially when truncated severely, in sharp contrast to POD-LB case, where the laminar state is found to be stable even with very low degrees of freedom. In the final presentation, a more detailed discussion will be provided for this comparison. An extra section will also be added to address the ROM constructed using a basis of balanced modes. |
Tuesday, November 26, 2024 2:08PM - 2:21PM |
ZC12.00007: FV-FluidAttentionNet: A Label-Free Physics-Informed Autoencoder with Finite-Volume Discretization for Rapid Navier-Stokes Solutions Mohammad Sarabian, Sudeep Sastry We present FV-FluidAttentionNet, a novel physics-informed autoencoder with attention mechanism for solving Navier-Stokes equations. This label-free surrogate model integrates finite-volume discretization within its computational graph, enabling fast GPU-based calculations of PDE residuals. Our approach significantly reduces computational time—by a factor of 1000 compared to conventional CFD solvers—while maintaining high accuracy. FV-FluidAttentionNet demonstrates exceptional performance in solving steady, incompressible Navier-Stokes equations for various scenarios, including 3D lid-driven cavity flow and flow past a cylinder at different Reynolds numbers. Notably, it excels in both interpolation and extrapolation, accurately predicting flow fields for non-dimensional parameters outside the training data. This generalization capability, combined with its speed and accuracy, positions FV-FluidAttentionNet as a transformative tool in computational fluid dynamics, offering potential for rapid, adaptive, and physically consistent simulations across diverse fluid dynamics applications. |
Tuesday, November 26, 2024 2:21PM - 2:34PM |
ZC12.00008: Enhanced Short-Term Precipitation Forecasting with Radar Data Using Swin Transformer Network Jun Park, Changhoon Lee Numerical Weather Prediction (NWP) systems integrate observational data from automatic weather station, upper air observation station, radar, and satellites through data assimilation to produce weather forecasts. However, the extensive computational demands of NWP models pose challenges for short-term predictions within a two-hour window. Among various observational data, radar data is directly correlated with atmospheric moisture particles and provides critical information for precipitation forecasting. In South Korea, radar data from 10 observation sites is combined to generate composite fields with a 5-minute interval and 500-meter spatial resolution. In this study, we developed a precipitation prediction model using a Swin Transformer-based network that directly utilizes radar data, bypassing the computationally intensive NWP models. Our research aimed to develop a model capable of predicting the next 18 consecutive precipitation fields based on the previous 4 consecutive fields. We compared our model's performance with the optical flow-based extrapolation method (pysteps) and the persistence model, using Root Mean Square Error (RMSE) as the evaluation metric. Results demonstrate that the Swin Transformer-based network outperforms both the optical flow and persistence models across all forecast time frames, indicating its robustness and accuracy in short-term precipitation prediction. |
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