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 C02: Interact: Machine Learning in Fluids |
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Chair: Karthikeyan Duraisamy, University of Michigan Room: 255 E |
Sunday, November 24, 2024 10:50AM - 11:20AM |
C02.00001: INTERACT FLASH TALKS: Machine Learning in Fluids Each Interact Flash Talk will last around 1 minute, followed by around 30 seconds of transition time. |
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C02.00002: Kinetic data-driven approach to turbulence subgrid modeling Alessandro Gabbana, Giulio Ortali, Nicola Demo, Gianluigi Rozza, Federico Toschi Recent advances in Machine Learning have opened up new perspectives for employing Artificial Neural Networks (ANNs) to enhance computational fluid dynamic solvers and develop data-driven turbulence models. In the context of Large Eddy Simulation (LES), ANNs have been used to establish subgrid scale (SGS) closure models from extensive datasets of fully resolved turbulent flows, leveraging their ability to handle high-dimensional and complex data. |
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C02.00003: Analyzing the transition-to-turbulence in Rayleigh-Benard flows through latent space representations Patricio Clark Di Leoni, Melisa Y Vinograd In the cusp of turbulence, Rayleigh-Benard flows exhibit both large-scale convective structures, as well as small-scale eddies. As the Rayleigh number is increased more scales become activated, synchronization properties between field components are lost, and, ultimately, the flow is dominated by the small-scale structures. By generating compressed latent representations of the phase space at each Rayleigh number via convolutional autoencoders we can track how the change in the number of degrees of freedom of the system, showing how during transition the rate of change is not linear. We then use these representations to analyze the properties of the flow. In particular, we estimate the entropy of the system and show how it grows as the system transitions to turbulence and the number of possible states increases. |
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C02.00004: Data-driven model reduction via non-intrusive optimization of projection operators and reduced-order dynamics Alberto Padovan, Blaine Vollmer, Daniel J Bodony Computing reduced-order models using non-intrusive methods is particularly attractive for systems that are simulated using black-box solvers. However, obtaining accurate data-driven models can be challenging, especially if the underlying systems exhibit large-amplitude transient growth. Although these systems may evolve near a low-dimensional subspace that can be easily identified using standard techniques such as Proper Orthogonal Decomposition (POD), computing accurate models often requires projecting the state onto this subspace via a non-orthogonal projection. While appropriate oblique projection operators can be computed using intrusive techniques that leverage the form of the underlying governing equations, purely data-driven methods currently tend to achieve dimensionality reduction via orthogonal projections, and this can lead to models with poor predictive accuracy. We address this issue by introducing a non-intrusive framework designed to simultaneously identify oblique projection operators and reduced-order dynamics. In particular, given training trajectories and assuming reduced-order dynamics of polynomial form, we fit a reduced-order model by solving an optimization problem over the product manifold of a Grassmann manifold, a Stiefel manifold, and several linear spaces (as many as the tensors that define the low-order dynamics). Furthermore, we show that the gradient of the cost function with respect to the optimization parameters can be conveniently written in closed form, so that there is no need for automatic differentiation. We compare our formulation with state-of-the-art methods on three examples: a three-dimensional system of ordinary differential equations, the complex Ginzburg-Landau (CGL) equation, and a two-dimensional lid-driven cavity flow at Reynolds number Re = 8300. |
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C02.00005: Conditioning deep learning on PDE parameters to generalise emulation of stochastic and chaotic dynamics Ira Jeet Singh Shokar, Peter H Haynes, Rich R Kerswell We introduce a probabilistic deep learning emulator for modeling stochastic and chaotic dynamical systems, conditioned on parameter values from the governing PDEs. Our approach involves pre-training on a fixed parameter domain and fine-tuning on a diverse, but crucially smaller dataset. This enables effective generalisation across a range of parameter values, maintaining robustness at interpolated values not seen during training. By incorporating local attention mechanisms, the network efficiently handles varying domain sizes, outperforming convolution kernels. This allows for computationally efficient pre-training on smaller domains, requiring limited data on larger domains to generalise to more turbulent regimes. We demonstrate our model's capabilities on quasi-geostrophic turbulence and the Kuramoto-Sivashinsky equation. The probabilistic nature of our model, along with significant computational speed-ups over traditional numerical integration, facilitates the efficient exploration of phase space and the statistical study of rare events. |
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C02.00006: Transition prediction in high-speed boundary layers using Bayesian deep operator networks Hannah Thompson, Yue Hao, Ponkrshnan Thiagarajan, Tamer A Zaki
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C02.00007: Integration of Temporal Dynamics in Graph U-Nets for Improved Mesh-Agnostic Spatio-Temporal Flow Prediction Sunwoong Yang, Yuning Wang, Abhijeet Vishwasrao, Ricardo Vinuesa, Namwoo Kang This study addresses the limitations of conventional deep-learning approaches based on convolutional neural networks, particularly their dependency on structured meshes, which restricts their applicability to complex geometries and unstructured meshes. Building on previous advancements in mesh-agnostic spatio-temporal prediction of transient flow fields using graph U-Nets, this work proposes further refinements by integrating temporal schemes commonly used in computational fluid dynamics (CFD). These enhancements aim to harmonize the machine learning framework with the physical principles of flow physics. Key objectives include improving accuracy and robustness in spatio-temporal flow predictions across diverse mesh configurations through the incorporation of temporal dynamics. The research will explore the effects of different temporal schemes on graph U-Net performance, identifying optimal configurations for enhanced predictive capabilities. The study will also investigate the impact of these enhancements on both transductive and inductive learning settings, aiming to accurately predict quantities for unseen nodes within trained graphs and generalize performance to new mesh configurations with varying flow conditions. This work aims to develop advanced graph U-Net models that integrate CFD temporal schemes, enhancing their applicability and reliability in real-world engineering applications involving complex fluid dynamics. |
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C02.00008: Multifidelity UQ strategies for laser-ignited rocket combustors Tony Zahtila, Davy Brouzet, Murray Cutforth, Diego Rossinelli, Gianluca Iaccarino In a rocket combustor, hydrodynamic ejection of a laser-induced plasma placed in a co-flowing fuel-oxidizer jet can facilitate re-ignition capability throughout a mission. The present work aims at understanding the various scenarios in which successful ignition may occur and builds probability distributions of ignition success and associated post-ignition pressure rise in the rocket chamber. In uncertainty space, this is a high-dimensional problem, and run-to-run variabilities arise from uncertainty in the deposited laser characteristics, and the stochastic nature of underlying turbulent mixing of propellants. A reduced order low-fidelity surrogate model is constructed that achieves a compression ratio of two orders of magnitude compared to the accurate high-fidelity simulations. This is accomplished by using a simplified chemistry mechanism and reduction in the simulation scale-resolution. Further, the surrogate model is constructed by means of an inverse problem in which deterministic processes from high-fidelity pilot cases are used to estimate the parameters in the low-fidelity space that map to high-fidelity counterparts. Thereafter, multi-fidelity Monte Carlo sampling is employed to obtain realizations of the uncertainty space. Finally, we present analysis of ignition likelihood and sensitivities. |
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C02.00009: Operator Learning for Reconstruction Problems: An Energy Transformer Approach with Applications in Fluid Mechanics Qian Zhang, George Em Karniadakis Machine learning methods have shown great success in various scientific areas, including fluid mechanics. However, reconstruction problems, where full data must be recovered from partial observations, remain challenging. In this paper, we propose a novel operator learning framework for solving reconstruction problems using the energy transformer. We formulate reconstruction as a mapping from incomplete observed data to full reconstructed data. The method is validated on three examples of fluid mechanics: 2D vortex street simulation, experimental jet impingement, and 3D turbulent jet flow. Results demonstrate the ability to accurately reconstruct complex flow fields from highly incomplete data (90\% missing), even for noisy experimental measurements, with fast training and inference on a single GPU. This work provides a promising new direction for tackling reconstruction problems in fluid mechanics and other scientific domains. |
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C02.00010: Learning Stochastic Closures via Conditional Diffusion Model and Neural Operator Xinghao Dong, Chuanqi Chen, Jinlong Wu Closure models are widely used in simulating complex multiscale dynamical systems such as turbulence and Earth's climate, for which direct numerical simulation that resolves all scales is often too expensive. For those systems without a clear scale separation, deterministic and local closure models often lack enough generalization capability, which limits their performance in many real-world applications. In this talk, we present a data-driven modeling framework for constructing stochastic and nonlocal closure models via conditional diffusion model and neural operator. Specifically, the Fourier neural operator is incorporated into a score-based diffusion model, which serves as a data-driven stochastic closure model for complex dynamical systems governed by partial differential equations (PDEs). We also demonstrate how accelerated sampling methods can improve the efficiency of the data-driven stochastic closure model. The results show that the proposed methodology provides a systematic approach via generative AI to constructing generalizable data-driven stochastic closure models for multiscale dynamical systems with continuous spatiotemporal fields. |
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C02.00011: Variational formulation of physics informed neural networks (vfPINN) Chinmay Katke, C. Nadir Kaplan Physics-informed neural networks (PINN) solve differential equations by minimizing a phenomenological loss function derived from these equations. However, higher-order derivatives in the differential equations describing many physical systems lead to higher computational costs. Additionally, solving coupled differential equations with PINN is complex due to manually or algorithmically determined ad hoc weight factors appearing in the loss function. We propose a variational PINN (vfPINN) algorithm that optimizes the functionals in integral form (e.g., Lagrangian, Hamiltonian, or Rayleighian) to address these issues. vfPINN naturally uses lower-order derivatives and replaces ad hoc weight factors with rigorous physical scales. Our simulations using vfPINN show promising results for benchmark systems like steady state Sine-Gordon equation and other ordinary differential equations (ODEs). We also explore the solution stability using the notion of conjugate points which are defined by a lack of positive definiteness in the second variation of the functional around the desired solution. Our ongoing research extends to locating conjugate points numerically in the domain and finding the corresponding unstable solutions using saddle point search algorithm that we developed for linear and non-linear ODEs. |
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C02.00012: Implicit Neural Representations Meets Interpretable Parameterized Mesh-agnostic Stability-Preserving Reduced-Order Modeling Weichao Li, Shaowu Pan Learning interpretable reduced-order models of nonlinear PDE dynamics in fluid dynamics has been a long-standing problem in the data-driven modeling of dynamical systems. Early works can be traced back to Operator Inference, Sparse Identification of Nonlinear Dynamics (SINDy), and SINDy-Autoencoder, among others. However, these approaches still suffer scalability issues in scalable nonlinear dimensionality reduction. On the other hand, novel dimensionality reduction frameworks that leverage implicit neural representation, such as Neural Implicit Flow, show great promise for scalable 3D PDE data, even on dynamic meshes. Here, we propose a novel framework combining the idea of implicit neural representation with learning interpretable nonlinear dynamics from data. We compare our framework against state-of-the-art operator learning techniques (e.g., FNO) and a recent related work called DINo that leverages a vanilla feedforward neural network to learn the nonlinear latent dynamics. Furthermore, we extend our interpretable reduced-order learning framework to a parametric setting. Our testing cases range from 2D wave propagation with varying wave speeds and forced 2D Navier-Stokes equations with varying viscosity to incompressible flow over a 2D cylinder with varying Reynolds numbers. |
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C02.00013: Geometry-informed deep learning surrogate models for flow prediction Nausheen Sultana Mehboob Basha, Mosayeb Shams, Sibo Cheng, Rossella Arcucci, Omar K Matar Deep learning surrogate models have gained popularity in flow prediction, but they face limitations with diverse geometries. This led to 'geometry-informed' models, which adapt and predict flows across various shapes, crucial for design optimisation, real-time predictions, and multi-fidelity frameworks [1]. |
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C02.00014: A real-time digital twin of nonlinear azimuthal thermoacoustics Andrea Nóvoa, Nicolas Noiray, James R Dawson, Luca Magri Predicting azimuthal thermoacoustic oscillations in real time is key to the safe operation of gas turbines and aeroengines. We propose a real-time digital twin of a hydrogen-fuelled laboratory annular combustor for different equivalence ratios. The digital twin is composed of (i) a deterministic physics-based low-order model, (ii) raw data from microphones at four azimuthal locations, and (iii) a data-driven tool that estimates biases. These three elements are statistically combined by the Regularized bias-aware Ensemble Kalman filter (r-EnKF) to infer states, parameters, and model errors (i.e., biases) in real time. The digital twin accurately predicts the azimuthal dynamics from raw acoustic data by leveraging data, physics, and estimates of the model bias, in contrast to the bias-unregularized ensemble Kalman filter. The proposed real-time digital twin generalizes existing low-order model methods because it enables the prediction of the fast-varying acoustic variables. Finally, the proposed framework infers all the system parameters simultaneously and allows the parameters to change over time as the acoustic dynamics vary. This work opens new opportunities for real-time digital twinning and low-order modelling, for example, turbulent flows, which are the subject of current research efforts. |
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C02.00015: CoNFiLD: Conditional Neural Field Latent Diffusion Model Generating Spatiotemporal Turbulence Pan Du, Meet H Parikh, Xiantao Fan, Xinyang Liu, Jian-Xun Wang This study presents the Conditional Neural Field Latent Diffusion (CoNFiLD) model, a novel generative AI method for rapid simulation of spatiotemporal chaotic/turbulent dynamics within three-dimensional irregular domains. Traditional eddy-resolved numerical simulations, despite offering detailed flow predictions, are limited by their extensive computational demands, restricting their broader engineering applications. In contrast, deep learning-based surrogate models promise efficient, data-driven solutions but often fall short in capturing the chaotic and stochastic nature of turbulence due to their reliance on deterministic frameworks. The CoNFiLD model addresses these challenges by integrating conditional neural field encoding with latent diffusion processes, enabling memory-efficient and robust probabilistic generation of spatiotemporal turbulence under varied conditions. Using Bayesian conditional sampling, the model adapts to diverse turbulence generation scenarios without retraining, covering zero-shot full-field flow reconstruction from sparse sensor measurements to super-resolution generation and spatiotemporal flow data restoration. Comprehensive numerical experiments on various inhomogeneous, anisotropic turbulent flows with irregular geometries have been conducted to evaluate the model's versatility and efficacy, showcasing its transformative potential in turbulence generation and broader spatiotemporal dynamics modeling. |
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C02.00016: ABSTRACT WITHDRAWN
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C02.00017: Ensemble Kalman Methods for Learning Closure Parameters Isabel Scherl, Eviatar Bach, Andrew Stuart, Tim Colonius Reynolds-average Navier-Stokes simulations require closure models to estimate Reynolds stresses. These closure models often contain adjustable model parameters. Estimating these parameters is a key step in implementing accurate and effective closure models in simulations. We demonstrate how techniques in data assimilation can be used to determine the optimal values of these parameters. The test case we use is the minimal flow unit, a channel simulation that is considered to be the smallest domain to sustain turbulent structures. As such, it has become a common test case for algorithmic development. Recent efforts have shown that ensemble Kalman methods can accurately and efficiently estimate system states. These techniques typically utilize observations and an ensemble of model realizations, with the goal of optimally combining these two data streams. Specifically, a method called ensemble Kalman inversion has been developed to iteratively optimize model parameters. This method has primarily been utilized in atmospheric modeling, however, we will demonstrate how this technique can be applied to a Reynolds-stress closure. |
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C02.00018: Information-Theoretic Buckingham-Pi Theorem: Application to Wall Model Discovery for Compressible Flow Over Roughness Yuan Yuan, Adrian Lozano-Duran Physical laws and models must rely on dimensionless variables. The Buckingham Pi theorem offers a systematic approach for obtaining dimensionless numbers for a given problem. However, these dimensionless numbers are not unique, as there is an infinite set of valid solutions. We introduce an information-theoretic, data-driven dimensional analysis method that identifies the best-performing dimensionless inputs to predict the non-dimensional quantity of interest. The approach is grounded in the information-theoretic bounds to the irreducible model error, which guarantees that the inputs identified maximize the predictability of the output regardless of the chosen modeling approach. The method involves the maximization of the mutual information between inputs and output, which is efficiently solved using the covariance matrix adaptation evolution strategy algorithm. We first validate the Information-Theoretic Buckingham Pi Theorem with a synthetic dataset with known scaling laws. Then, the dimensional learning is applied to discover a wall model for compressible flows over rough walls using a recent DNS database. The best dimensionless inputs and outputs for the wall model are utilized to train an artificial neural network model able to predict wall shear stress and heat flux within 10% accuracy. |
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C02.00019: LUCIE: A Lightweight Uncoupled ClImate Emulator with long-term stability and physical consistency for O(1000)-member ensembles Ashesh K Chattopadhyay, Romit Maulik, Haiwen Guan, Troy Arcomano We present LUCIE, a 1000- member ensemble data-driven atmospheric emulator that remains stable during autoregressive inference for thousands of years without a drifting climatology. LUCIE has been trained on 9.5 years of coarse-resolution ERA5 data with 4 prognostic variables on a single A100 GPU for 2.4 h. Owing to the cheap computational cost of inference, 1000 model ensembles are executed for 5 years to compute an uncertainty-quantified climatology for the prognostic variables that closely match the climatology obtained from ERA5. Unlike all the other state-of-the-art AI weather models, LUCIE is neither unstable nor does it produce hallucinations that result in unphysical drift of the emulated climate. Furthermore, LUCIE does not impose``true" sea-surface temperature (SST) from a coupled numerical model to enforce the annual cycle in temperature. We demonstrate the long-term climatology obtained from LUCIE as well as subseasonal-to-seasonal scale prediction skills on the prognostic variables. |
Sunday, November 24, 2024 11:20AM - 12:50PM |
C02.00020: INTERACT DISCUSSION SESSION WITH POSTERS: Machine Learning in Fluids After each Flash Talk has concluded, the Interact session will be followed by interactive poster or e-poster presentations, with plenty of time for one-on-one and small group discussions. |
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C02.00021: Abstract Withdrawn
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C02.00022: Abstract Withdrawn |
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