Kevin Potter
Georgia Institute of Technology
AutoencoderAlgorithmPhysical systemLinear subspaceGraph (abstract data type)Supervised learningNonlinear dimensionality reductionConvolutionArtificial intelligenceComplex geometryTest setPattern recognitionMNIST databaseOverfittingModel order reductionNonlinear manifoldPolygon meshMathematicsWord error rateComputer scienceDelaunay triangulationDiscretizationContextual image classificationConvolutional neural networkPartial differential equation
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#1Kevin Potter (Georgia Institute of Technology)H-Index: 2
#2Steven Richard Sleder (SNL: Sandia National Laboratories)
Last. John Tencer (SNL: Sandia National Laboratories)H-Index: 6
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We present a novel graph convolutional layer that is fast, conceptually simple, and provides high accuracy with reduced overfitting. Based on pseudo-differential operators, our layer operates on graphs with relative position information available for each pair of connected nodes. We evaluate our method on a variety of supervised learning tasks, including superpixel image classification using the MNIST, CIFAR10, and CIFAR100 superpixel datasets, node correspondence using the FAUST dataset, and sh...
We propose a nonlinear manifold learning technique based on deep convolutional autoencoders that is appropriate for model order reduction of physical systems in complex geometries. Convolutional neural networks have proven to be highly advantageous for compressing data arising from systems demonstrating a slow-decaying Kolmogorov n-width. However, these networks are restricted to data on structured meshes. Unstructured meshes are often required for performing analyses of real systems with comple...
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We propose a nonlinear manifold learning technique based on deep autoencoders that is appropriate for model order reduction of physical systems in complex geometries. Convolutional neural networks have proven to be highly advantageous for systems demonstrating a slow-decaying Kolmogorov n-width. However, these networks are restricted to data on structured meshes. Unstructured meshes are often required for performing analyses of real systems with complex geometry. Our custom graph convolution ope...
5 Citations