Publications

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Graph neural networks (GNNs) are an emerging model for learning graph embeddings and making predictions on graph structured data. However, robustness of graph neural networks is not yet well-understood. In this work, we focus on node structural identity predictions, where a representative GNN model is able to achieve near-perfect accuracy. We also show that the same GNN model is not robust to addition of structural noise, through a controlled dataset and set of experiments. Finally, we show that under the right conditions, graph-augmented training is capable of significantly improving robustness to structural noise.

As computer architectures are rapidly evolving (e.g. those designed for exascale), multiple portability frameworks have been developed to avoid new architecture-specific development and tuning. However, portability frameworks depend on compilers for auto-vectorization and may lack support for explicit vectorization on heterogeneous platforms. Alternatively, programmers can use intrinsics-based primitives to achieve more efficient vectorization, but the lack of a gpu back-end for these primitives makes such code non-portable. A unified, portable, Single Instruction Multiple Data (simd) primitive proposed in this work, allows intrinsics-based vectorization on cpus and many-core architectures such as Intel Knights Landing (knl), and also facilitates Single Instruction Multiple Threads (simt) based execution on gpus. This unified primitive, coupled with the Kokkos portability ecosystem, makes it possible to develop explicitly vectorized code, which is portable across heterogeneous platforms. The new simd primitive is used on different architectures to test the performance boost against hard-to-auto-vectorize baseline, to measure the overhead against efficiently vectroized baseline, and to evaluate the new feature called the “logical vector length” (lvl). The simd primitive provides portability across cpus and gpus without any performance degradation being observed experimentally.

This article describes a parallel implementation of a two-level overlapping Schwarz preconditioner with the GDSW (Generalized Dryja–Smith–Widlund) coarse space described in previous work [12, 10, 15] into the Trilinos framework; cf. [16]. The software is a significant improvement of a previous implementation [12]; see Sec. 4 for results on the improved performance.

We propose a new algorithm for the fast solution of large, sparse, symmetric positive-definite linear systems, spaND (sparsified Nested Dissection). It is based on nested dissection, sparsification, and low-rank compression. After eliminating all interiors at a given level of the elimination tree, the algorithm sparsifies all separators corresponding to the interiors. This operation reduces the size of the separators by eliminating some degrees of freedom but without introducing any fill-in. This is done at the expense of a small and controllable approximation error. The result is an approximate factorization that can be used as an efficient preconditioner. We then perform several numerical experiments to evaluate this algorithm. We demonstrate that a version using orthogonal factorization and block-diagonal scaling takes fewer CG iterations to converge than previous similar algorithms on various kinds of problems. Furthermore, this algorithm is provably guaranteed to never break down and the matrix stays symmetric positive-definite throughout the process. We evaluate the algorithm on some large problems show it exhibits near-linear scaling. The factorization time is roughly \scrO (N), and the number of iterations grows slowly with N.

This article describes a parallel implementation of a two-level overlapping Schwarz preconditioner with the GDSW (Generalized Dryja–Smith–Widlund) coarse space described in previous work [12, 10, 15] into the Trilinos framework; cf. [16]. The software is a significant improvement of a previous implementation [12]; see Sec. 4 for results on the improved performance.

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Community detection in graphs is a canonical social network analysis method. We consider the problem of generating suites of teras-cale synthetic social networks to compare the solution quality of parallel community-detection methods. The standard method, based on the graph generator of Lancichinetti, Fortunato, and Radicchi (LFR), has been used extensively for modest-scale graphs, but has inherent scalability limitations. We provide an alternative, based on the scalable Block Two-Level Erdos-Renyi (BTER) graph generator, that enables HPC-scale evaluation of solution quality in the style of LFR. Our approach varies community coherence, and retains other important properties. Our methods can scale real-world networks, e.g., to create a version of the Friendster network that is 512 times larger. With BTER's inherent scalability, we can generate a 15-terabyte graph (4.6B vertices, 925B edges) in just over one minute. We demonstrate our capability by showing that label-propagation community-detection algorithm can be strong-scaled with negligible solution-quality loss.

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