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 J01: Minisymposia: Reduced-Order Modeling in Fluids Via Artificial and Human Intelligence |
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Chair: George Haller, ETH Zurich Room: Sagamore 123 |
Sunday, November 20, 2022 4:35PM - 5:01PM |
J01.00001: Some aspects of combined equation- and data-driven modeling for turbulent flows Invited Speaker: Beverley J McKeon Significant recent progress has been made in flow modeling using both equation-driven and data-driven techniques. We focus here on the intersection of these two approaches, using data to complete the details of known flow dynamics. In turbulent flows, nonlinear effects can prevent linear data-driven techniques such as dynamic mode decomposition (Schmid, 2010) and data-driven resolvent analysis (Hermann et al, 2021) from identifying the correct underlying linear operator governing the dynamics. In this talk we will review some of the aspects of learning and exploiting linear and nonlinear dynamics from equations and from data recently explored by the authors. |
Sunday, November 20, 2022 5:01PM - 5:27PM |
J01.00002: Likelihood-weighted active learning with application to Bayesian optimization and uncertainty quantification for complex fluid flows Invited Speaker: Themistoklis Sapsis Analysis of physical and engineering systems, especially those related to fluids, is characterized by unique computational challenges associated with high dimensionality of parameter spaces, large cost of simulations or experiments, as well as existence of uncertainty. For a wide range of these problems the goal is to either quantify uncertainty and compute risk for critical events, optimize parameters or control strategies, and/or making decisions. Bayesian active learning provides a flexible framework for performing these tasks. However, Bayesian calculations are often prohibitively expensive in terms of the required simulations or experiments, even in the active learning setting. In this talk we introduce a new class of acquisition functions that utilize a likelihood-weighted ratio that accounts for the importance of the output relative to the input. This ratio acts essentially as a probabilistic sampling weight and guides the sampling algorithm towards regions of the input space where the objective function assumes abnormal values, resulting in significant savings of computational or experimental resources needed for convergence. We show that the adopted acquisition functions can be rigorously derived as the asymptotic limit of an optimal acquisition function that has a minimax form over a functional space. Subsequently, we demonstrate their favorable properties compared to standard methods on benchmark functions commonly used in the optimization community as well as real world applications involving turbulence, fluid-structure interaction problems and optimal sensor placement. |
Sunday, November 20, 2022 5:27PM - 5:53PM |
J01.00003: New computational methods for the dynamical systems view of turbulence Invited Speaker: Jacob Page Over the last three decades ideas from dynamical systems theory have significantly advanced our understanding of transitional and weakly turbulent shear flows. In this perspective, the evolution of a turbulent flow is considered as a trajectory in a very high-dimensional dynamical system `pinballing' between unstable exact coherent states (ECS). Applying these ideas to turbulent flows at high Re has the potential to advance our understanding of the role of individual dynamical processes in producing the well-known statistical results (e.g. the cascade) and brings new opportunities for modelling and control. However, progress has stalled due to both an inability to identify guesses for candidate ECS and the poor performance of the Newton-Raphson methods used for convergence. In this talk I will discuss new approaches to both of these problems built on ideas from machine learning, using two-dimensional Kolmogorov flow as an example. First, I will show how deep convolutional autoencoders can be employed to learn low-dimensional representations of the flow which are closely related to ECS. These latent representations form a robust observable with which to measure near recurrences on turbulent orbits, leading to the discovery of an order of magnitude more periodic orbits than standard methods, including a large number of new solutions associated with intermittent, high-dissipation bursts. I will then describe how the requirements for a near recurrence can be removed altogether using a fully-differentiable flow solver (Kochkov et al, Proc. Nat. Acad. Sci. 118, 2021), where periodic orbits with specific properties can be sought via gradient descent on an appropriate loss function. This new method yields large numbers of periodic orbits at high Re, where past methods have found only a handful of structures. Time permitting, I will also discuss data-driven methods for weighting the collection of ECS to estimate flow statistics in an approach akin to periodic orbit theory. |
Sunday, November 20, 2022 5:53PM - 6:19PM |
J01.00004: Machine Learning for Scientific Discovery Invited Speaker: Steven L Brunton This work describes how machine learning may be used to develop accurate and efficient nonlinear dynamical systems models for complex natural and engineered systems. We explore the sparse identification of nonlinear dynamics (SINDy) algorithm, which identifies a minimal dynamical system model that balances model complexity with accuracy, avoiding overfitting. This approach tends to promote models that are interpretable and generalizable, capturing the essential "physics" of the system. We also discuss the importance of learning effective coordinate systems in which the dynamics may be expected to be sparse. This sparse modeling approach will be demonstrated on a range of challenging modeling problems in fluid dynamics, and we will discuss how to incorporate these models into existing model-based control efforts. Because fluid dynamics is central to transportation, health, and defense systems, we will emphasize the importance of machine learning solutions that are interpretable, explainable, generalizable, and that respect known physics. |
Sunday, November 20, 2022 6:19PM - 6:45PM |
J01.00005: Modes, Manifolds and Clusters—Different flavours of reduced-order models Invited Speaker: Bernd R Noack Since over a century, reduced-order models (ROM) are at the heart of theoretical fluid dynamics thanks to their paramount importance for physical understanding, data compression, estimation, control and optimization. In this talk, we exemplify different ROM approaches for the fluidic pinball [1,2,3] , the wake flow behind a cluster of three parallel cylinders on an equilateral triangle pointing upstream. The flow may be actuated by rotating cylinders. First, the transition scenario of the unforced fluidic pinball is modeled with a five-mode sparse Galerkin model. This model comprises successive Hopf and pitch-fork bifucations, which are typical for a number of wake flows. Second, a feature-based manifold-fold model [4] is identified describing transient and post-transient flow dynamics more accurate and more low-dimensional than the Galerkin model. Third, a cluster-based network model (CNM) [5] is presented describing the fluidic pinball wake with actuation as free input, employing thousand differently actuated pinball simulations. CNM yields a robust dynamics from a fully automatable procedure. Finally, other applications and a broader perspective of ROM is provided. |
Sunday, November 20, 2022 6:45PM - 7:11PM |
J01.00006: Data-driven Flow Models from Nonlinear Spectral Reduction Invited Speaker: George Haller Most fluid flows of practical importance admit coexisting steady, periodic of quasiperiodic stationary states, as well as transitions amomg them. No single linearized model can capture such characteristically nonlinear behavior, which explains why reduced-orders for even classic flows, such as Couette and Rayleigh-Bernard flows. have been unavailable. For the same reason, no data-driven modeling approach among the available linear ones has been able to accurately describe characteristically nonlinear fluid-structure interactions problems, such as vortex shedding behind a cylinder or fluid sloshing in a tank. |
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