Deep learning of vortex-induced vibrations

By Maizar Raissi, Zhicheng Wang, Michael S. Triantafyllou, G. Em Karniadakis. 2018

440 citations recorded by the source corpus.

Vortex-induced vibrations of bluff bodies occur when the vortex shedding frequency is close to the natural frequency of the structure. Of interest is the prediction of the lift and drag forces on the structure given some limited and scattered information on the velocity field. This is an inverse problem that is not straightforward to solve using standard computational fluid dynamics methods, especially since no information is provided for the pressure. An even greater challenge is to infer the lift and drag forces given some dye or smoke visualizations of the flow field. Here we employ deep neural networks that are extended to encode the incompressible Navier–Stokes equations coupled with the structure’s dynamic motion equation. In the first case, given scattered data in space–time on the velocity field and the structure’s motion, we use four coupled deep neural networks to infer very accurately the structural parameters, the entire time-dependent pressure field (with no prior training data), and reconstruct the velocity vector field and the structure’s dynamic motion. In the second case, given scattered data in space–time on a concentration field only, we use five coupled deep neural networks to infer very accurately the vector velocity field and all other quantities of interest as before. This new paradigm of inference in fluid mechanics for coupled multi-physics problems enables velocity and pressure quantification from flow snapshots in small subdomains and can be exploited for flow control applications and also for system identification.

Subfields: Computational Mechanics, Statistical and Nonlinear Physics

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Citations in the corpus

Physics informed deep learning for computational elastodynamics without labeled data (2020, background): “btained through minimization of the network’s loss function, which typically consists of the residual error of the governing equations along with initial/boundary values. More recently, Raissi et al. [9,10,15,16] has inherited and extended this concept, leveraged the strong expressibility of DNNs, a”
Physics-informed neural networks (PINNs) for fluid mechanics: a review (2021, background): “Physics-informed learning [7], introduced in a series of papers by Karniadakis’s group both for Gaussian-process regression [8,9] and physics-informed neural networks (PINNs) [10], can seamlessly integrate multifidelity/multi-”
Physics-informed neural networks for inverse problems in supersonic flows (2022, methodology): “In recent years physics-informed neural networks (PINNs) [1] emerged as an alternative simple method to solve many problems in computational science and engineering, see, for example [2, 3, 4, 5, 6, 7, 8, 9, 10, 4, 11, 12, 13, 14, 15].”
Variational Physics-Informed Neural Networks For Solving Partial Differential Equations (2019, background): “The recent development of PINNs has been well established for forward and inverse problem of solving di ﬀ erential equations [30, 32, 39, 29] and since then a number of extensions has been made to tackle several physical and biomedical problems [28, 18, 19].”
CAN-PINN: A Fast Physics-Informed Neural Network Based on Coupled-Automatic-Numerical Differentiation Method (2021, methodology): “PINNs have been demonstrated for various physics phenomena, including heat transfer [23,24], fluid dynamics [25–27] and electromagnetic propagation [28–30].”
NSFnets (Navier-Stokes flow nets): Physics-informed neural networks for the incompressible Navier-Stokes equations (2020, methodology): “This approach has also been used to simulate vortex induced vibrations in [16] and also to tackle ill-posed inverse ﬂuid mechanics problems, a framework called “hidden ﬂuid me-chanics” presented in [17].”
When and why PINNs fail to train: A neural tangent kernel perspective (2020, background): “…already led to a series of remarkable results across a range of problems in computational science and engineering, including ﬂuids mechanics [1, 2, 4, 5], bio-engineering [6, 7], meta-material design [8, 9, 10], free boundary problems [11], Bayesian networks and uncertainty quantiﬁcation [12, 13,…”
Adaptive activation functions accelerate convergence in deep and physics-informed neural networks (2019, methodology): “In the PINN algorithm various activation functions such as tanh, sin etc are used to solve various problems, see [25, 28] for more details.”
Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks (2019, background): “This simple and easy to program algorithm has been shown to be successful for diverse problems in physics and ﬂuid mechanics [5, 6, 7], especially for inverse problems and even for discovering hidden physics [8].”
Physics-informed deep learning for incompressible laminar flows (2020, background): “[5, 6] introduced a general framework of physics-informed neural network (PINN) and demonstrated its capacity in modeling complex physical systems such as solving/identifying”