1,653 research outputs found
Practical quality control tools for curves and surfaces
Curves (geometry) and surfaces created by Computer Aided Geometric Design systems in the engineering environment must satisfy two basic quality criteria: the geometric shape must have the desired engineering properties; and the objects must be parameterized in a way which does not cause computational difficulty for geometric processing and engineering analysis. Interactive techniques are described which are in use at Boeing to evaluate the quality of aircraft geometry prior to Computational Fluid Dynamic analysis, including newly developed methods for examining surface parameterization and its effects
08221 Abstracts Collection -- Geometric Modeling
From May 26 to May 30 2008 the Dagstuhl Seminar 08221 ``Geometric Modeling\u27\u27 was held in the International Conference and Research Center (IBFI),
Schloss Dagstuhl.
During the seminar, several participants presented their current
research, and ongoing work and open problems were discussed. Abstracts of
the presentations given during the seminar as well as abstracts of
seminar results and ideas are put together in this paper. The first section
describes the seminar topics and goals in general.
Links to extended abstracts or full papers are provided, if available
DeepSphere: Efficient spherical Convolutional Neural Network with HEALPix sampling for cosmological applications
Convolutional Neural Networks (CNNs) are a cornerstone of the Deep Learning
toolbox and have led to many breakthroughs in Artificial Intelligence. These
networks have mostly been developed for regular Euclidean domains such as those
supporting images, audio, or video. Because of their success, CNN-based methods
are becoming increasingly popular in Cosmology. Cosmological data often comes
as spherical maps, which make the use of the traditional CNNs more complicated.
The commonly used pixelization scheme for spherical maps is the Hierarchical
Equal Area isoLatitude Pixelisation (HEALPix). We present a spherical CNN for
analysis of full and partial HEALPix maps, which we call DeepSphere. The
spherical CNN is constructed by representing the sphere as a graph. Graphs are
versatile data structures that can act as a discrete representation of a
continuous manifold. Using the graph-based representation, we define many of
the standard CNN operations, such as convolution and pooling. With filters
restricted to being radial, our convolutions are equivariant to rotation on the
sphere, and DeepSphere can be made invariant or equivariant to rotation. This
way, DeepSphere is a special case of a graph CNN, tailored to the HEALPix
sampling of the sphere. This approach is computationally more efficient than
using spherical harmonics to perform convolutions. We demonstrate the method on
a classification problem of weak lensing mass maps from two cosmological models
and compare the performance of the CNN with that of two baseline classifiers.
The results show that the performance of DeepSphere is always superior or equal
to both of these baselines. For high noise levels and for data covering only a
smaller fraction of the sphere, DeepSphere achieves typically 10% better
classification accuracy than those baselines. Finally, we show how learned
filters can be visualized to introspect the neural network.Comment: arXiv admin note: text overlap with arXiv:astro-ph/0409513 by other
author
Towards a Unified Framework for Fair and Stable Graph Representation Learning
As the representations output by Graph Neural Networks (GNNs) are
increasingly employed in real-world applications, it becomes important to
ensure that these representations are fair and stable. In this work, we
establish a key connection between counterfactual fairness and stability and
leverage it to propose a novel framework, NIFTY (uNIfying Fairness and
stabiliTY), which can be used with any GNN to learn fair and stable
representations. We introduce a novel objective function that simultaneously
accounts for fairness and stability and develop a layer-wise weight
normalization using the Lipschitz constant to enhance neural message passing in
GNNs. In doing so, we enforce fairness and stability both in the objective
function as well as in the GNN architecture. Further, we show theoretically
that our layer-wise weight normalization promotes counterfactual fairness and
stability in the resulting representations. We introduce three new graph
datasets comprising of high-stakes decisions in criminal justice and financial
lending domains. Extensive experimentation with the above datasets demonstrates
the efficacy of our framework.Comment: Accepted to UAI'2
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