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Data management is becoming increasingly important in dealing with the large amounts of data produced by large-scale scientific simulations and instruments. Existing multilevel compression algorithms offer a promising way to manage scientific data at scale, but may suffer from relatively low performance and reduction quality. In this paper, we propose MGARD+, a multilevel data reduction and refactoring framework drawing on previous multilevel methods, to achieve high-performance data decomposition and high-quality error-bounded lossy compression. Our contributions are four-fold: 1) We propose a level-wise coefficient quantization method, which uses different error tolerances to quantize the multilevel coefficients. 2) We propose an adaptive decomposition method which treats the multilevel decomposition as a preconditioner and terminates the decomposition process at an appropriate level. 3) We leverage a set of algorithmic optimization strategies to significantly improve the performance of multilevel decomposition/recomposition. 4) We evaluate our proposed method using four real-world scientific datasets and compare with several state-of-the-art lossy compressors. Experiments demonstrate that our optimizations improve the decomposition/recomposition performance of the existing multilevel method by up to 70X, and the proposed compression method can improve compression ratio by up to 2X compared with other state-of-the-art error-bounded lossy compressors under the same level of data distortion.

The cost of I/O is a significant challenge on current supercomputers, and the trend is likely to continue into the foreseeable future. This challenge is amplified in scientific visualization because of the requirement to consume large amounts of data before processing can begin. Lossy compression has become an important technique in reducing the cost of performing I/O. In this paper we consider the implications of using compressed data for visualization within a scientific workflow. We use visualization operations on simulation data that is reduced using three different state-of-the-art compression techniques. We study the storage efficiency and preservation of visualization features on the resulting compressed data, and draw comparisons between the three techniques used. Our contributions can help inform both scientists and researchers in the use and design of compression techniques for preservation of important visualization details.

A crude but commonly used technique for compressing ordered scientific data consists of simply retaining every $s$th datum (with a value of $s=10$ generally the default) and discarding the remainder. Should the value of a discarded datum be required afterwards, an approximation is generated by linear interpolation of the two nearest retained values. Despite the widespread use of this and similar techniques, there is little by way of theoretical analysis of their expected performance. First, we quantify the accuracy achieved by linear interpolation when approximating values discarded by decimation, obtaining both deterministic bounds in terms of appropriate smoothness measures of the data and probabilistic bounds in terms of statistics of the data. Second, we investigate the efficiency of the lossless compression scheme consisting of decimation coupled with encoding of the interpolation errors. In particular, we bound the expected compression ratio in terms of the appropriate measures of the data. Finally,...

With the growing computational complexity of science and the complexity of new and emerging hardware, it is time to re-evaluate the traditional monolithic design of computational codes. One new paradigm is constructing larger scientific computational experiments from the coupling of multiple individual scientific applications, each targeting their own physics, characteristic lengths, and/or scales. We present a framework constructed by leveraging capabilities such as in-memory communications, workflow scheduling on HPC resources, and continuous performance monitoring. This code coupling capability is demonstrated by a fusion science scenario, where differences between the plasma at the edges and at the core of a device have different physical descriptions. This infrastructure not only enables the coupling of the physics components, but it also connects in situ or online analysis, compression, and visualization that accelerate the time between a run and the analysis of the science content. Results from runs on Titan and Cori are presented as a demonstration.

As we continue toward exascale, scientific data volume is continuing to scale and becoming more burdensome to manage. In this paper, we lay out opportunities to enhance state of the art data management techniques. We emphasize well-principled data compression, and using it to achieve progressive refinement. This can both accelerate I/O and afford the user increased flexibility when she interacts with the data. The formulation naturally maps onto enabling partitioning of the progressively improving-quality representations of a data quantity into different media-type destinations, to keep the highest priority information as close as possible to the computation, and take advantage of deepening memory/storage hierarchies in ways not previously possible. Careful monitoring is requisite to our vision, not only to verify that compression has not eliminated salient features in the data, but also to better understand the performance of massively parallel scientific applications. Increased mathematical rigor would be ideal,to help bring compression on a better-understood theoretical footing, closer to the relevant scientific theory, more aware of constraints imposed by the science, and more tightly error-controlled. Throughout, we highlight pathfinding research we have begun exploring related these topics, and comment toward future work that will be needed.

We use a polyhedral criterion for the existence of diagonal splittings to investigate which toric varieties X are diagonally split. Our results are stated in terms of the vector configuration given by primitive generators of the 1-dimensional cones in the fan defining X. We show, in particular, that X is diagonally split at all q if and only if this configuration is unimodular, and X is not diagonally split at any q if this configuration is not 2-regular. We also study implications for the possibilities for the set of q at which a toric variety X is diagonally split., Comment: 11 pages v2: minor revisions, to appear in Proc. Amer. Math. Soc

Chapter ten, written by Ben Whitney, the educational welfare specialist officer for Staffordshire Country Council, addresses the legal regulation of child labour and criticises the existing legislation. Whitney advocates for a more accessible framework of laws and regulation that will aid children in their transition from childhood (school) to adulthood (work).

Rapid growth in scientific data and a widening gap between computational speed and I/O bandwidth make it increasingly infeasible to store and share all data produced by scientific simulations. Instead, we need methods for reducing data volumes: ideally, methods that can scale data volumes adaptively so as to enable negotiation of performance and fidelity tradeoffs in different situations. Multigrid-based hierarchical data representations hold promise as a solution to this problem, allowing for flexible conversion between different fidelities so that, for example, data can be created at high fidelity and then transferred or stored at lower fidelity via logically simple and mathematically sound operations. However, the effective use of such representations has been hindered until now by the relatively high costs of creating, accessing, reducing, and otherwise operating on such representations. We describe here highly optimized data refactoring kernels for GPU accelerators that enable efficient creation and manipulation of data in multigrid-based hierarchical forms. We demonstrate that our optimized design can achieve up to 250 TB/s aggregated data refactoring throughput—83% of theoretical peak—on 1024 nodes of the Summit supercomputer. We showcase our optimized design by applying it to a large-scale scientific visualization workflow and the MGARD lossy compression software.