1,638 research outputs found
Structured Sequence Modeling with Graph Convolutional Recurrent Networks
This paper introduces Graph Convolutional Recurrent Network (GCRN), a deep
learning model able to predict structured sequences of data. Precisely, GCRN is
a generalization of classical recurrent neural networks (RNN) to data
structured by an arbitrary graph. Such structured sequences can represent
series of frames in videos, spatio-temporal measurements on a network of
sensors, or random walks on a vocabulary graph for natural language modeling.
The proposed model combines convolutional neural networks (CNN) on graphs to
identify spatial structures and RNN to find dynamic patterns. We study two
possible architectures of GCRN, and apply the models to two practical problems:
predicting moving MNIST data, and modeling natural language with the Penn
Treebank dataset. Experiments show that exploiting simultaneously graph spatial
and dynamic information about data can improve both precision and learning
speed
The Topology ToolKit
This system paper presents the Topology ToolKit (TTK), a software platform
designed for topological data analysis in scientific visualization. TTK
provides a unified, generic, efficient, and robust implementation of key
algorithms for the topological analysis of scalar data, including: critical
points, integral lines, persistence diagrams, persistence curves, merge trees,
contour trees, Morse-Smale complexes, fiber surfaces, continuous scatterplots,
Jacobi sets, Reeb spaces, and more. TTK is easily accessible to end users due
to a tight integration with ParaView. It is also easily accessible to
developers through a variety of bindings (Python, VTK/C++) for fast prototyping
or through direct, dependence-free, C++, to ease integration into pre-existing
complex systems. While developing TTK, we faced several algorithmic and
software engineering challenges, which we document in this paper. In
particular, we present an algorithm for the construction of a discrete gradient
that complies to the critical points extracted in the piecewise-linear setting.
This algorithm guarantees a combinatorial consistency across the topological
abstractions supported by TTK, and importantly, a unified implementation of
topological data simplification for multi-scale exploration and analysis. We
also present a cached triangulation data structure, that supports time
efficient and generic traversals, which self-adjusts its memory usage on demand
for input simplicial meshes and which implicitly emulates a triangulation for
regular grids with no memory overhead. Finally, we describe an original
software architecture, which guarantees memory efficient and direct accesses to
TTK features, while still allowing for researchers powerful and easy bindings
and extensions. TTK is open source (BSD license) and its code, online
documentation and video tutorials are available on TTK's website
Segmentation of Unstructured Datasets
Datasets generated by computer simulations and experiments in Computational Fluid Dynamics tend to be extremely large and complex. It is difficult to visualize these datasets using standard techniques like Volume Rendering and Ray Casting. Object Segmentation provides a technique to extract and quantify regions of interest within these massive datasets. This thesis explores basic algorithms to extract coherent amorphous regions from two-dimensional and three-dimensional scalar unstructured grids. The techniques are applied to datasets from Computational Fluid Dynamics and from Finite Element Analysis
Scientific visualizations
Visualizations for three different categories of problems are presented: measurements of object parameters as they vary over time, constructing surfaces from unorganized sets of points, and representing the internal structure of volumes using isosurfaces. Problem backgrounds are discussed as well as the operational details of each visualization. Visualizations were written with ease of use in mind for Spiegel, a programmable visualization environment
Compiling global name-space programs for distributed execution
Distributed memory machines do not provide hardware support for a global address space. Thus programmers are forced to partition the data across the memories of the architecture and use explicit message passing to communicate data between processors. The compiler support required to allow programmers to express their algorithms using a global name-space is examined. A general method is presented for analysis of a high level source program and along with its translation to a set of independently executing tasks communicating via messages. If the compiler has enough information, this translation can be carried out at compile-time. Otherwise run-time code is generated to implement the required data movement. The analysis required in both situations is described and the performance of the generated code on the Intel iPSC/2 is presented
Phase behavior and morphology of multicomponent liquid mixtures
Multicomponent systems are ubiquitous in nature and industry. While the
physics of few-component liquid mixtures (i.e., binary and ternary ones) is
well-understood and routinely taught in undergraduate courses, the
thermodynamic and kinetic properties of -component mixtures with have
remained relatively unexplored. An example of such a mixture is provided by the
intracellular fluid, in which protein-rich droplets phase separate into
distinct membraneless organelles. In this work, we investigate equilibrium
phase behavior and morphology of -component liquid mixtures within the
Flory-Huggins theory of regular solutions. In order to determine the number of
coexisting phases and their compositions, we developed a new algorithm for
constructing complete phase diagrams, based on numerical convexification of the
discretized free energy landscape. Together with a Cahn-Hilliard approach for
kinetics, we employ this method to study mixtures with and
components. We report on both the coarsening behavior of such systems, as well
as the resulting morphologies in three spatial dimensions. We discuss how the
number of coexisting phases and their compositions can be extracted with
Principal Component Analysis (PCA) and K-Means clustering algorithms. Finally,
we discuss how one can reverse engineer the interaction parameters and volume
fractions of components in order to achieve a range of desired packing
structures, such as nested `Russian dolls' and encapsulated Janus droplets.Comment: 16 pages, 11 figures + hyperlinks to 7 video
Mining Point Cloud Local Structures by Kernel Correlation and Graph Pooling
Unlike on images, semantic learning on 3D point clouds using a deep network
is challenging due to the naturally unordered data structure. Among existing
works, PointNet has achieved promising results by directly learning on point
sets. However, it does not take full advantage of a point's local neighborhood
that contains fine-grained structural information which turns out to be helpful
towards better semantic learning. In this regard, we present two new operations
to improve PointNet with a more efficient exploitation of local structures. The
first one focuses on local 3D geometric structures. In analogy to a convolution
kernel for images, we define a point-set kernel as a set of learnable 3D points
that jointly respond to a set of neighboring data points according to their
geometric affinities measured by kernel correlation, adapted from a similar
technique for point cloud registration. The second one exploits local
high-dimensional feature structures by recursive feature aggregation on a
nearest-neighbor-graph computed from 3D positions. Experiments show that our
network can efficiently capture local information and robustly achieve better
performances on major datasets. Our code is available at
http://www.merl.com/research/license#KCNetComment: Accepted in CVPR'18. *indicates equal contributio
A Distributed-Memory Randomized Structured Multifrontal Method for Sparse Direct Solutions
We design a distributed-memory randomized structured multifrontal solver for large sparse matrices. Two layers of hierarchical tree parallelism are used. A sequence of innovative parallel methods are developed for randomized structured frontal matrix operations, structured update matrix computation, skinny extend-add operation, selected entry extraction from structured matrices, etc. Several strategies are proposed to reuse computations and reduce communications. Unlike an earlier parallel structured multifrontal method that still involves large dense intermediate matrices, our parallel solver performs the major operations in terms of skinny matrices and fully structured forms. It thus significantly enhances the efficiency and scalability. Systematic communication cost analysis shows that the numbers of words are reduced by factors of about in two dimensions and about in three dimensions, where is the matrix size and is an off-diagonal numerical rank bound of the intermediate frontal matrices. The efficiency and parallel performance are demonstrated with the solution of some large discretized PDEs in two and three dimensions. Nice scalability and significant savings in the cost and memory can be observed from the weak and strong scaling tests, especially for some 3D problems discretized on unstructured meshes
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