Turbulence

By Victor Montagud-Camps. 2019

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Citations in the corpus

Data-driven discovery of partial differential equations (2016, methodology): “Traditionally, an ODE is then identified on the coefficients of these energetic modes, resulting in a model that resembles a Galerkin projection onto POD modes [14].”
Convex integration and phenomenologies in turbulence (2019, methodology): “(6)It is typical in certain laboratory measurements to recast measurements from the time domain into the space domain by appealing to the Taylor hypothesis [81].”
Statistical Solutions of Hyperbolic Conservation Laws: Foundations (2016, background): “(This general rule is known as Isserlis’ theorem [36]; see also [30, p. 44].)”
Ergodic Theory, Dynamic Mode Decomposition, and Computation of Spectral Properties of the Koopman Operator (2016, background): “It is known that for finite-dimensional observables on discretetime dynamical systems, POD reduces to SVD [15].”
Sparse identification of nonlinear dynamics for model predictive control in the low-data limit (2017, background): “Since fluids data is typically high-dimensional, DMD is built on the proper orthogonal decomposition (POD) [19], effectively recombining POD modes in a linear combination to enforce the temporal coherence.”
Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systems (2019, methodology): “The basis for the reduced space is computed from data; a 15 common choice is the Proper Orthogonal Decomposition (POD) basis, com16 prised of the leading principal components of the data [1, 2, 3, 4].”
Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders (2018, methodology): “This includes the reduced-basis technique [62, 67] and proper orthogonal decomposition (POD) [37, 15] for parameterized stationary problems; balanced truncation [54], rational interpolation [4, 32], and Craig–Bampton model reduction [20] for linear time invariant (LTI) systems; and Galerkin projecti”
Temperature in and out of equilibrium: A review of concepts, tools and attempts (2017, background): “small k where the energy is injected, to small scale, where the energy is dissipated by the molecular viscosity [194,195,185].”
Projection-based model reduction: Formulations for physics-based machine learning (2019, methodology): “, the proper orthogonal decomposition (POD) [9, 10, 11], perhaps the most widely used model reduction method, is very closely related to the principal component analysis).”
Frontiers of chaotic advection (2014, background): “The classical and more well-known way to do that is through turbulence: by imposing a very high Reynolds number (Re = UL/ν) in a 3D flow, we trigger the formation of a Kolmogorov energy cascade (Frisch, 1996; Kolmogorov, 1941a,b) whereby energy flows from large to small scales.”
Linearly-Recurrent Autoencoder Networks for Learning Dynamics (2017, background): “The length L = 8π was chosen where the equation first begins to exhibit chaotic dynamics [9].”
Machine Learning Control – Taming Nonlinear Dynamics and Turbulence (2016, background): “This cascade connects large-scale energy carrying anisotropic coherent structures with nearly isotropic small-scale dissipative structures over many orders of magnitudes in scale [106].”