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Manifold (fluid mechanics)

About: Manifold (fluid mechanics) is a research topic. Over the lifetime, 13223 publications have been published within this topic receiving 123959 citations. The topic is also known as: Intake manifold.


Papers
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Journal ArticleDOI
02 Sep 2018
TL;DR: Uniform Manifold Approximation and Projection (UMAP) is a dimension reduction technique that can be used for visualisation similarly to t-SNE, but also for general non-linear dimension reduction.
Abstract: Uniform Manifold Approximation and Projection (UMAP) is a dimension reduction technique that can be used for visualisation similarly to t-SNE, but also for general non-linear dimension reduction. UMAP has a rigorous mathematical foundation, but is simple to use, with a scikit-learn compatible API. UMAP is among the fastest manifold learning implementations available – significantly faster than most t-SNE implementations.

4,141 citations

Book ChapterDOI
Mikio Sato1
TL;DR: In this paper, the authors interpreted the time evolution of a solution as the dynamical motion of a point on a Grassmann manifold, and a generic solution corresponds to a generic point whose orbit (in the infinitely many time variables) is dense in the manifold, whereas degenerate solutions corresponding to points bound on those closed submanifolds that are stable under the time evolve describe the solutions to various specialized equations, such as KdV, Boussinesq, nonlinear Schrodinger, and sine-Gordon.
Abstract: Publisher Summary Soliton Equations as Dynamical Systems on Infinite Dimensional Grassmann Manifold The totality of the solutions of the Kadomtsev– Petviashvili equation as well as of its multicomponent generalization forms an infinite dimensional Grassmann manifold. In this picture, the time evolution of a solution is interpreted as the dynamical motion of a point on this manifold. A generic solution corresponds to a generic point whose orbit (in the infinitely many time variables) is dense in the manifold, whereas degenerate solutions corresponding to points bound on those closed submanifolds that are stable under the time evolution describe the solutions to various specialized equations, such as KdV, Boussinesq, nonlinear Schrodinger, and sine-Gordon.

835 citations

Journal ArticleDOI
TL;DR: In this article, it was shown that the classical dynamics of several slowly moving monopoles corresponds to a geodesic motion in the manifold of exact, static multi-monopole configurations.

753 citations

Journal ArticleDOI
11 Jul 2016
TL;DR: A framework to synthesize character movements based on high level parameters, such that the produced movements respect the manifold of human motion, trained on a large motion capture dataset, can produce smooth, high quality motion sequences without any manual pre-processing of the training data.
Abstract: We present a framework to synthesize character movements based on high level parameters, such that the produced movements respect the manifold of human motion, trained on a large motion capture dataset. The learned motion manifold, which is represented by the hidden units of a convolutional autoencoder, represents motion data in sparse components which can be combined to produce a wide range of complex movements. To map from high level parameters to the motion manifold, we stack a deep feedforward neural network on top of the trained autoencoder. This network is trained to produce realistic motion sequences from parameters such as a curve over the terrain that the character should follow, or a target location for punching and kicking. The feedforward control network and the motion manifold are trained independently, allowing the user to easily switch between feedforward networks according to the desired interface, without re-training the motion manifold. Once motion is generated it can be edited by performing optimization in the space of the motion manifold. This allows for imposing kinematic constraints, or transforming the style of the motion, while ensuring the edited motion remains natural. As a result, the system can produce smooth, high quality motion sequences without any manual pre-processing of the training data.

542 citations


Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023959
20222,095
2021520
2020586
2019578
2018543