Representing turbulent statistics with partitions of state space. Part 1. Theory and methodology
AN Souza - Journal of Fluid Mechanics, 2024 - cambridge.org
This is the first of a two-part paper. We formulate a data-driven method for constructing finite-
volume discretizations of an arbitrary dynamical system's underlying Liouville/Fokker …
volume discretizations of an arbitrary dynamical system's underlying Liouville/Fokker …
Representing turbulent statistics with partitions of state space. Part 2. The compressible Euler equations
AN Souza - Journal of Fluid Mechanics, 2024 - cambridge.org
This is the second part of a two-part paper. We apply the methodology of the first paper
(Souza, J. Fluid Mech., vol. 997, 2024, A1) to construct a data-driven finite-volume …
(Souza, J. Fluid Mech., vol. 997, 2024, A1) to construct a data-driven finite-volume …
A Koopman–Takens theorem: Linear least squares prediction of nonlinear time series
The least squares linear filter, also called the Wiener filter, is a popular tool to predict the
next element (s) of time series by linear combination of time-delayed observations. We …
next element (s) of time series by linear combination of time-delayed observations. We …
Accurate estimates of dynamical statistics using memory
Many chemical reactions and molecular processes occur on time scales that are significantly
longer than those accessible by direct simulations. One successful approach to estimating …
longer than those accessible by direct simulations. One successful approach to estimating …
Physics-informed machine learning with smoothed particle hydrodynamics: Hierarchy of reduced Lagrangian models of turbulence
Building efficient, accurate, and generalizable reduced-order models of developed
turbulence remains a major challenge. This manuscript approaches this problem by …
turbulence remains a major challenge. This manuscript approaches this problem by …
Data-driven Mori-Zwanzig: Approaching a reduced order model for hypersonic boundary layer transition
View Video Presentation: https://doi. org/10.2514/6.2023-1624. vid In this work, we apply, for
the first time to spatially inhomogeneous flows, a recently developed data-driven learning …
the first time to spatially inhomogeneous flows, a recently developed data-driven learning …
Data-Driven Mori-Zwanzig: Reduced Order Modeling of Sparse Sensors Measurements for Boundary Layer Transition
View Video Presentation: https://doi. org/10.2514/6.2023-4256. vid Understanding,
predicting and controlling laminar-turbulent boundary-layer transition is crucial for the next …
predicting and controlling laminar-turbulent boundary-layer transition is crucial for the next …
[图书][B] The Method of Distributions for Random Ordinary Differential Equations
TE Maltba - 2023 - search.proquest.com
Random ordinary differential equations (RODEs) describe numerous physical and biological
systems whose dynamics contain some level of inherent randomness. These sources of …
systems whose dynamics contain some level of inherent randomness. These sources of …
Mori-Zwanzig Modal Decomposition
We introduce the Mori-Zwanzig (MZ) Modal Decomposition (MZMD), a novel technique for
performing modal analysis of large scale spatio-temporal structures in complex dynamical …
performing modal analysis of large scale spatio-temporal structures in complex dynamical …
Featuring Koopman Mode Decomposition
D Aristoff, J Copperman, N Mankovich… - arXiv preprint arXiv …, 2023 - arxiv.org
This article introduces an advanced Koopman mode decomposition (KMD) technique--
coined Featurized Koopman Mode Decomposition (FKMD)--that uses time embedding and …
coined Featurized Koopman Mode Decomposition (FKMD)--that uses time embedding and …