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Lifting MGARD: Construction of (pre)wavelets on the interval using polynomial predictors of arbitrary order

MGARD (MultiGrid Adaptive Reduction of Data) is an algorithm for compressing and refactoring scientific data, based on the theory of multigrid methods. The core algorithm is built around stable multilevel decompositions of conforming piecewise linear $C^0$ finite element spaces, enabling accurate error control in various norms and derived quantities of interest. In this work, we extend this construction to arbitrary order Lagrange finite elements $\mathbb{Q}_p$, $p \geq 0$, and propose a reformulation of the algorithm as a lifting scheme with polynomial predictors of arbitrary order. Additionally, a new formulation using a compactly supported wavelet basis is discussed, and an explicit construction of the proposed wavelet transform for uniform dyadic grids is described.

Reshniak, Viktor [Oak Ridge National Laboratory (O↗

Improving Progressive Retrieval for HPC Scientific Data using Deep Neural Network

As the disparity between compute and I/O on high-performance computing systems has continued to widen, it has become increasingly difficult to perform post-hoc data analytics on full-resolution scientific simulation data due to the high I/O cost. Error-bounded data decomposition and progressive data retrieval framework has recently been developed to address such a challenge by performing data decomposition before storage and reading only part of the decomposed data when necessary. However, the performance of the progressive retrieval framework has been suffering from the over-pessimistic error control theory, such that the achieved maximum error of recomposed data is significantly lower than the required error. Therefore, more data than required is fetched for recomposition, incurring additional I/O overhead. In order to tackle this issue, we propose a DNN-based progressive retrieval framework that can better identify the minimum amount of data to be retrieved. Our contributions are as follows: 1) We provide an in-depth investigation of the recently developed progressive retrieval framework; 2) We propose two designs of prediction models (named D-MGARD and E-MGARD) to estimate the amount of retrieved data size based on error bounds. 3) We evaluate our proposed solutions using scientific datasets generated by real-world simulations from two domains. Evaluation results demonstrate the effectiveness of our solution in accurately predicting the amount of retrieval data size, as well as the advantages of our solution over the traditional approach to reducing the I/O overhead. Based on our evaluation, our solution is shown to read significantly less data (5% - 40% with D-MGARD, 20% - 80% with E-MGARD).

Wang, Jinzhen↗

Optimising the processing and storage of visibilities using lossy compression

The next-generation radio astronomy instruments are providing a massive increase in sensitivity and coverage, largely through increasing the number of stations in the array and the frequency span sampled. The two primary problems encountered when processing the resultant avalanche of data are the need for abundant storage and the constraints imposed by I/O, as I/O bandwidths drop significantly on cold storage. An example of this is the data deluge expected from the SKA Telescopes of more than 60 PB per day, all to be stored on the buffer filesystem. While compressing the data is an obvious solution, the impacts on the final data products are hard to predict. In this paper, we chose an error-controlled compressor – MGARD – and applied it to simulated SKA-Mid and real pathfinder visibility data, in noise-free and noise-dominated regimes. As the data have an implicit error level in the system temperature, using an error bound in compression provides a natural metric for compression. MGARD ensures the compression incurred errors adhere to the user-prescribed tolerance. To measure the degradation of images reconstructed using the lossy compressed data, we proposed a list of diagnostic measures, exploring the trade-off between these error bounds and the corresponding compression ratios, as well as the impact on science quality derived from the lossy compressed data products through a series of experiments. We studied the global and local impacts on the output images for continuum and spectral line examples. We found relative error bounds of as much as 10%, which provide compression ratios of about 20, have a limited impact on the continuum imaging as the increased noise is less than the image RMS, whereas a 1% error bound (compression ratio of 8) introduces an increase in noise of about an order of magnitude less than the image RMS. For extremely sensitive observations and for very precious data, we would recommend a 0.1% error bound with compression ratios of about 4. These have noise impacts two orders of magnitude less than the image RMS levels. At these levels, the limits are due to instabilities in the deconvolution methods. We compared the results to the alternative compression tool DYSCO, in both the impacts on the images and in the relative flexibility. MGARD provides better compression for similar error bounds and has a host of potentially powerful additional features.

Techniques: interferometric↗

Scientific Data Compression for Large Scale Computational Fluid Dynamics (CFD) Simulations

This Cooperative Research and Development Agreement (CRADA) between Oak Ridge National Laboratory (ORNL) and General Electric (GE) investigated methods for reducing the size of large computational fluid dynamics (CFD) simulation datasets using scientific data compression techniques. The work focused on adapting the MultiGrid Adaptive Reduction of Data (MGARD) compression framework and integrating it with high-performance I/O and visualization tools used in CFD workflows. MGARD uses hierarchical multilevel decomposition to enable error-controlled compression of floating-point scientific data while preserving quantities of interest. During the project, MGARD compression was integrated with the ADIOS I/O framework and visualization tools such as ParaView to enable efficient storage, transfer, and analysis of simulation data. The collaboration also explored approaches for improving compression performance for CFD data defined on unstructured meshes. Results demonstrate that scientific data compression can significantly reduce storage requirements and improve data management for large-scale CFD simulations.

97 MATHEMATICS AND COMPUTING↗

Maintaining Trust in Reduction: Preserving the Accuracy of Quantities of Interest for Lossy Compression

As the growth of data sizes continues to outpace computational resources, there is a pressing need for data reduction techniques that can significantly reduce the amount of data and quantify the error incurred in compression. Compressing scientific data presents many challenges for reduction techniques since it is often on non-uniform or unstructured meshes, is from a high-dimensional space, and has many Quantities of Interests (QoIs) that need to be preserved. To illustrate these challenges, we focus on data from a large scale fusion code, XGC. XGC uses a Particle-In-Cell (PIC) technique which generates hundreds of PetaBytes (PBs) of data a day, from thousands of timesteps. XGC uses an unstructured mesh, and needs to compute many QoIs from the raw data, f.One critical aspect of the reduction is that we need to ensure that QoIs derived from the data (density, temperature, flux surface averaged momentums, etc.) maintain a relative high accuracy. We show that by compressing XGC data on the high-dimensional, nonuniform grid on which the data is defined, and adaptively quantizing the decomposed coefficients based on the characteristics of the QoIs, the compression ratios at various error tolerances obtained using a multilevel compressor (MGARD) increases more than ten times. We then present how to mathematically guarantee that the accuracy of the QoIs computed from the reduced f is preserved during the compression. We show that the error in the XGC density can be kept under a user-specified tolerance over 1000 timesteps of simulation using the mathematical QoI error control theory of MGARD, whereas traditional error control on the data to be reduced does not guarantee the accuracy of the QoIs.

Gong, Qian↗

Tuning the Interpolation Basis in a Multigrid Decomposition for Local Error Control

In the compression of scientific data, error-controlled compressors enable to considerably decrease the size of the dataset while maintaining adequate levels of accuracy. In this paper, we note that multi-level refactoring scheme such as MGARD i) rely on an approximation of the data based on the interpolation of coefficients, ii) estimate the resulting error with global metrics on the dataset. To improve on these two aspects, we propose a method that aims to divide the original dataset into blocks based on their smoothness and refactors each block separately with the most relevant interpolation order. We show the relevance of such a method on tailored datasets and the benefits and challenges when applying it to large scientific data.

Vidal, Nicolas [ORNL]↗

A Framework for Compressing Unstructured Scientific Data via Serialization

We present a general framework for compressing unstructured scientific data with known local connectivity. A common application is simulation data defined on arbitrary finite element meshes. The framework employs a greedy topology preserving reordering of original nodes which allows for seamless integration into existing data processing pipelines. This reordering process depends solely on mesh connectivity and can be performed offline for optimal efficiency. However, the algorithm’s greedy nature also supports on-the-fly implementation. The proposed method is compatible with any compression algorithm that leverages spatial correlations within the data. The effectiveness of this approach is demonstrated on a large-scale real dataset using several compression methods, including MGARD, SZ, and ZFP.

Reshniak, Viktor [ORNL] (ORCID:0000000315454462)↗

Unbalanced Parallel I/O: An Often-Neglected Side Effect of Lossy Scientific Data Compression

Lossy compression techniques have demonstrated promising results in significantly reducing the scientific data size while guaranteeing the compression error bounds. However, one important yet often neglected side effect of lossy scientific data compression is its impact on the performance of parallel I/O. Our key observation is that the compressed data size is often highly skewed across processes in lossy scientific compression. To understand this behavior, we conduct extensive experiments where we apply three lossy compressors MGARD, ZFP, and SZ, which are specifically designed and optimized for scientific data, to three real-world scientific applications Gray-Scott simulation, WarpX, and XGC. Our analysis result demonstrates that the size of the compressed data is always skewed even if the original data is evenly decomposed among processes. Such skewness widely exists in different scientific applications using different compressors as long as the information density of the data varies across processes. We then systematically study how this side effect of lossy scientific data compression impacts the performance of parallel I/O. We observe that the skewness in the sizes of the compressed data often leads to I/O imbalance, which can significantly reduce the efficiency of I/O bandwidth utilization if not properly handled. In addition, writing data concurrently to a single shared file through MPI-IO library is more sensitive to the unbalanced I/O loads. Therefore, we believe our research community should pay more attention to the unbalanced parallel I/O caused by lossy scientific data compression.

Wang, Xinying↗

Efficient Data Compression for 3D Sparse TPC via Bicephalous Convolutional Autoencoder

Real-time data collection and analysis in large experimental facilities present a great challenge across multiple domains, including high energy physics, nuclear physics, and cosmology. To address this, machine learning (ML)-based methods for real-time data compression have drawn significant attention. However, unlike natural image data, such as CIFAR and ImageNet that are relatively small-sized and continuous, scientific data often come in as three-dimensional 3D data volumes at high rates with high sparsity (many zeros) and non-Gaussian value distribution. This makes direct application of popular ML compression methods, as well as conventional data compression methods, suboptimal. To address these obstacles, this work introduces a dual-head autoencoder to resolve sparsity and regression simultaneously, called Bicephalous Convolutional AutoEncoder (BCAE). This method shows advantages both in compression fidelity and ratio compared to traditional data compression methods, such as MGARD, SZ, and ZFP. To achieve similar fidelity, the best performer among the traditional methods can reach only half the compression ratio of BCAE. Moreover, a thorough ablation study of the BCAE method shows that a dedicated segmentation decoder improves the reconstruction.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Accelerating Multigrid-based Hierarchical Scientific Data Refactoring on GPUs

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.

Data refactoring↗

OptZConfig: Efficient Parallel Optimization of Lossy Compression Configuration

Lossless compressors have very low compression ratios that do not meet the needs of today's large-scale scientific applications that produce vast volumes of data. Error-bounded lossy compression (EBLC) is considered a critical technique for the success of scientific research. Although EBLC allows users to set an error bound for the compression, users have been unable to specify the requirements on the compression quality, limiting practical use. Our contributions are: (1) We formulate the problem of configuring EBLC to preserve a user-defined metric as an optimization problem. This allows many classes of new metrics to be preserved, which improves over current practices. (2) We present a framework, OptZConfig, that can adapt to improvements in the search algorithm, compressor, and metrics with minimal changes, enabling future advancements in this area. (3) We demonstrate the advantages of our approach against the leading methods to configure compressors to preserve specific metrics. Here, our approach improves compression ratios against a specialized compressor by up to 3 x, has a 56x speedup over FRaZ, 1000x speedup over MGARD-QOI post tuning, and 110x speedup over systematic approaches which had not been bounded by compressors before.

97 MATHEMATICS AND COMPUTING↗

Multilevel Techniques for Compression and Reduction of Scientific Data---The Multivariate Case

We develop a technique for multigrid adaptive reduction of data (MGARD). Special attention is given to the case of tensor product grids, where our approach permits the use of nonuniformly spaced grids in each direction, which can prove problematic for many types of data reduction methods. An important feature of our approach is the provision of guaranteed, computable bounds on the loss incurred by the reduction of the data. Many users are leery of lossy algorithms and will only consider using them provided that numerical bounds on the pointwise difference between the original and the reduced datasets are given. Accordingly, we develop techniques for bounding the loss measured in the $L^{\infty}(\Omega)$ norm, and we show that these bounds are realistic in the sense that they do not significantly overestimate the actual loss. Here, the resulting loss indicators are used to guide the adaptive reduction of the data so that the reduced dataset meets a user-prescribed tolerance or memory constraint. Illustrative numerical examples, including the reduction of data arising from the simulation of a nonlinear reaction-diffusion problem, a turbulent channel flow, and a climate simulation, are provided.

97 MATHEMATICS AND COMPUTING↗

Multilevel Techniques for Compression and Reduction of Scientific Data-Quantitative Control of Accuracy in Derived Quantities

Although many compression algorithms are focused on preserving pointwise values of the data, application scientists are generally more concerned with derived quantities. Equally well, the user may even be willing to accept a high level of lossiness in the compression provided that the compressed data respect certain invariants, such as mass conservation. In the current work, we develop a mathematical framework and techniques that enable data to be adaptively compressed while maintaining a specified tolerance on a class of user-prescribed quantities. Here, the algorithm is used to augment the functionality of the data reduction package MGARD developed in previous work and the functionality is illustrated by a range of application including data from computational simulation of autocatalytic reaction simulation, turbulent combustion simulation, experimental data obtained from magnetic confinement fusion experiment, and simulation of turbulent flow along a rectangular channel. In each case, we consider one or more relevant quantities of interest and reduce the data so as to preserve these quantities.

97 MATHEMATICS AND COMPUTING↗

Fast 2D Bicephalous Convolutional Autoencoder for Compressing 3D Time Projection Chamber Data

High-energy large-scale particle colliders produce data at high speed in the order of 1 terabytes per second in nuclear physics and petabytes per second in high energy physics. Developing real-time data compression algorithms to reduce such data at high throughput to fit permanent storage has drawn increasing attention. Specifically, at the newly constructed sPHENIX experiment at the Relativistic Heavy Ion Collider (RHIC), a time projection chamber is used as the main tracking detector, which records particle trajectories in a volume of three-dimensional (3D) cylinder. The resulting data are usually very sparse with occupancy around 10.8%. Such sparsity presents a challenge to conventional learning-free lossy compression algorithms, such as SZ, ZFP, and MGARD. The 3D convolutional neural network (CNN)-based approach, Bicephalous Convolutional Autoencoder (BCAE), outperforms traditional methods both in compression rate and reconstruction accuracy. BCAE can also utilize the computation power of graphical processing units suitable for deployment in a modern heterogeneous highperformance computing environment. This work introduces two BCAE variants: BCAE++ and BCAE-2D. BCAE++ achieves a 15% better compression ratio and a 77% better reconstruction accuracy measured in mean absolute error compared with BCAE. BCAE-2D treats the radial direction as the channel dimension of an image, resulting in a 3× speedup in compression throughput. In addition, we demonstrate an unbalanced autoencoder with a larger decoder can improve reconstruction accuracy without significantly sacrificing throughput. Lastly, we observe both the BCAE++ and BCAE-2D can benefit more from using half-precision mode in throughput (76 - 79% increase) without loss in reconstruction accuracy. The source code and links to data and pretrained models can be found at https://github.com/BNL-DAQ-LDRD/NeuralCompression_v2

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

CODARcode/MGARD

MGARD is a software providing error-controlled lossy compression and data refactoring based on multi-grid theories. It transforms floating-point scientific data into a multilevel representation, followed by quantization and lossless encoding processes, resulting in a self-describing compressed buffer. It supports diverse data topologies, error control norms, and computing architectures.

Chen, Jieyang [University of Oregon]↗

Accelerating Multigrid-based Hierarchical Scientific Data Refactoring on GPUs

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.

Chen, Jieyang↗

Scalable Hybrid Learning Techniques for Scientific Data Compression

Data compression is becoming critical for storing scientific data because many scientific applications need to store large amounts of data and post process this data for scientific discovery. Unlike image and video compression algorithms that limit errors to primary data (PD), scientists require compression techniques that accurately preserve derived quantities of interest (QoIs). Here, this article presents a physics-informed compression technique implemented as an end-to-end, scalable, GPU-based pipeline for data compression that addresses this requirement. Our hybrid compression technique combines machine learning techniques and standard compression methods. Specifically, we combine an autoencoder, an error-bounded lossy compressor to provide guarantees on raw data error, and a constraint satisfaction post-processing step to preserve the QoIs within a minimal error (generally less than floating point error). The effectiveness of the data compression pipeline is demonstrated by compressing nuclear fusion simulation data generated by a large-scale fusion code, XGC, which produces hundreds of terabytes of data in a single day. Our approach works within the ADIOS framework and results in compression by a factor of more than 150 while requiring only a few percent of the computational resources necessary for generating the data, making the overall approach highly effective for practical scenarios.

ITER↗