3,084 research outputs found
Geometric deep learning: going beyond Euclidean data
Many scientific fields study data with an underlying structure that is a
non-Euclidean space. Some examples include social networks in computational
social sciences, sensor networks in communications, functional networks in
brain imaging, regulatory networks in genetics, and meshed surfaces in computer
graphics. In many applications, such geometric data are large and complex (in
the case of social networks, on the scale of billions), and are natural targets
for machine learning techniques. In particular, we would like to use deep
neural networks, which have recently proven to be powerful tools for a broad
range of problems from computer vision, natural language processing, and audio
analysis. However, these tools have been most successful on data with an
underlying Euclidean or grid-like structure, and in cases where the invariances
of these structures are built into networks used to model them. Geometric deep
learning is an umbrella term for emerging techniques attempting to generalize
(structured) deep neural models to non-Euclidean domains such as graphs and
manifolds. The purpose of this paper is to overview different examples of
geometric deep learning problems and present available solutions, key
difficulties, applications, and future research directions in this nascent
field
Master of Science
thesisIt is common to extract isosurfaces from simulation eld data to visualize and gain understanding of the underlying physical phenomenon being simulated. As the input parameters of the simulation change, the resulting isosurface varies, and there has been increased interest in quantifying and visualization of these variations as part of the larger interest in uncertainty quantification. In this thesis, we propose an analysis and visualization pipeline for examining the intrinsic variation in isosurfaces caused by simulation parameter perturbation. Drawing inspiration from the shape modeling community, we incorporate the use of heat-kernel signatures (HKS) with a simple nite-difference approach for quantifying the degree to which a region (or even a point) on an isosurface has undergone intrinsic change. Coupled with a clustering technique and the use of color maps, our pipeline allows the user to select the level of fidelity with which they wish to evaluate and visualize the amount of intrinsic change. The pipeline is described with a simple example to walk the reader through the different steps, and experimental validation of parameter choices in the pipeline is provided to justify our design. Then we present canonical and simulation examples to demonstrate the pipeline's use in different applications
Weight-Aware Implicit Geometry Reconstruction with Curvature-Guided Sampling
Neural surface implicit representations offer numerous advantages, including
the ability to easily modify topology and surface resolution. However,
reconstructing implicit geometry representation with only limited known data is
challenging. In this paper, we present an approach that effectively
interpolates and extrapolates within training points, generating additional
training data to reconstruct a surface with superior qualitative and
quantitative results. We also introduce a technique that efficiently calculates
differentiable geometric properties, i.e., mean and Gaussian curvatures, to
enhance the sampling process during training. Additionally, we propose a
weight-aware implicit neural representation that not only streamlines surface
extraction but also extend to non-closed surfaces by depicting non-closed areas
as locally degenerated patches, thereby mitigating the drawbacks of the
previous assumption in implicit neural representations.Comment: 9 page
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