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Both a solid model (for CAD) and a non-manifold model (for CAE) are immediately extracted from the master model through a selection process.

Then, thanks to the approach here adopted, an integral manifold model is derived, suitable for advanced control system design.

Simply put, we can view a manifold as a low-dimensional nonlinear surface within ℝ N. Manifold models arise, for example, in settings where a low-dimensional parameter controls the generation of the signal (see Figure 2).

All of this suggests that manifolds may be viable models to use in CS recovery; see [18] for additional discussion on the topic of using manifold models to recover individual signals.

PEC utilizes a Pareto efficiency, and introduces a manifold drift term as a measure for determining the adequacy of using a certain combustion-manifold model to predict selected quantities of interest.

Thus, although we may be able to posit sparse and manifold-based models for concisely capturing the intra- and inter-signal structures among the images in the ensemble, directly exploiting these models for the purpose of data compression may be prohibitively complex or require expensive collaboration among the sensors.

A new manifold-based reduced order model for nonlinear problems in multiscale modeling of heterogeneous hyperelastic materials is presented.

Two different model manifolds were designed, one model for which the vortices are described with Gaussian profiles, and another in which a more optimal spatial structure is used.

Then we present a non-linear tensor decomposition method that integrates the two manifolds into a generative model for multi-view shape modeling, as shown in Figure 2. Figure 2 Illustration of the generative model for shape interpolation along the view manifold (the blue trajectory) and given some points on the identity manifold.

A numerical model for a porous manifold has been developed to study its effects on thermal stratification in a typical storage tank.

The potential reasons for the different predictive utility of the model for patient outcomes are manifold.

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