MGARD (MultiGrid Adaptive Reduction of Data) is a technique for multilevel lossy compression and refactoring of scientific data based on the theory of multigrid methods. We encourage you to make a GitHub issue if you run into any problems using MGARD, have any questions or suggestions, etc.

MGARD framework consists of the following modules. Please see the detailed instructions for each module to build and install MGARD.

MGARD-CPU: MGARD compression implementation for CPUs

MGARD-CPU is designed for running compression on CPUs. See the detailed user guide here. In addition, MGARD-CPU can be configured to preserve region-of-interest (RoI user guide) and linear quantity-of-interest (QoI user guide) during data compression.

MGARD-X: Accelerated and portable compression

MGARD-X is designed for portable compression on NVIDIA GPUs, AMD GPUs, and CPUs. See the detailed user guide here. In addition, MGARD-X can be configured to preserve region-of-interest (ROI user guide) and linear quantity-of-interest (QoI user guide) during data compression.

MGARD$\text{-}\lambda$: Preserving Non-Linear Quantity-of-Interest

MGARD$\text{-}\lambda$ is specifically designed for preserving non-linear quantity-of-interest during data compression. This is an experimental part of MGARD. Currently, it only supports certain QoIs derived from XGC 5D data. See theory in here and example in here.

MDR/MDR-X: Fine-grain progressive data reconstruction

MDR and MDR-X are designed to enable fine-grain data refactoring and progressive data reconstruction. See the detailed user guide here.

Self-describing format for compressed and refactored data

Data produced by MGARD, MGARD-X, and MDR-X are designed to follow a unified self-describing format. See format details in here.

Version history

Detailed release notes (features added, changes, and bug fixes) are linked below for each version.

• MGARD 1.7.0 (Sep. 2026) — Delivered HP-MDR, a high-performance MDR-X refactoring and reconstruction pipeline; introduced BlockMGARD, a block-based hybrid hierarchy compression pipeline with region-of-interest support; deprecated and removed the legacy standalone MGARD-CUDA backend in favor of MGARD-X; added new rANS and BlockDelta lossless backends and a portable warp-cooperative LZ4 implementation; added Blackwell (sm_120) GPU build support; numerous performance improvements and bug fixes.
• MGARD 1.6.0 (Aug. 2025) — Redesigned the compression/decompression pipeline for higher end-to-end throughput; improved OpenMP and Huffman CPU performance and ZSTD linking; removed the prefetch option (now always enabled) and the coordinate-normalization build option; fixed issues with LZ4 compression, thread safety, MDR-X L2 error control, ADIOS2 integration, and HIP builds.
• MGARD 1.5.2 (Sep. 2023) — Added compression status reporting to the high-level API, an ADIOS2 operator build example, autotuning for Huffman kernels, asynchronous LZ4/Zstd compression, a pipeline optimized for compressing time-series data, and improved memory-usage estimation; fixed bugs in Huffman codebook generation, the domain decomposer, reduced-memory-footprint mode, and MDR-X reconstruction.
• MGARD 1.5.0 (Apr. 2023) — Added the MGARD$\text{-}\lambda$ pipeline for preserving non-linear QoIs in XGC data and the MGARD-RoI pipeline for region-of-interest preservation; added a GPU pipeline for out-of-core, large-scale compression; added Apple Silicon (ARM) support; fixed issues with CUDA (older versions and 12+), the NVIDIA HPC SDK, MDR-X compilation, and linear quantization overflow.
• MGARD 1.4.0 (Jan. 2023) — Added multi-device support for compression/decompression, RuntimeX, and Array; added workspace pre-allocation, a new OpenMP backend, block-based domain decomposition, and high-level MDR-X APIs; modularized the compression and refactoring workflows; reduced build time via optional autotuning; fixed bugs affecting GCC 9, Huffman encoding synchronization, Xcode, and the SYCL backend.
• MGARD 1.3.0 (Sep. 2022) — Introduced MGARD-X: portable compression for CPU (serial and multi-threaded), NVIDIA GPUs, AMD GPUs, and Intel GPUs, with a self-describing format, automatic domain decomposition, multi-GPU parallel compression, and high-/low-level APIs. Introduced MDR-X for portable multi-precision data refactoring on CPU and GPU.
• MGARD 1.0.0 (Sep. 2021) — Improved CPU compression/decompression speed (iterator optimizations, index precomputation, memory-access-pattern improvements); added OpenMP parallelization; added a self-describing command-line executable and high-level APIs; added support pluggable lossless compressors; fixed several multilevel-decomposition bugs.
• MGARD 0.1.0 (Sep. 2020) — Added initial support for unstructured data; restructured code for extensibility; added Nvidia GPU support for 2D/3D; added Huffman entropy encoding and ZSTD integration; added FP64 support; added continuous integration (Travis CI).
• MGARD 0.0.0.2 (Sep. 2019) — Initial public release. Lossy compression with preservation of $L_\infty$, $L_2$ and S-norm on primary data, and linear QoIs; added FP32 support.

Publications

The following works either contribute to the MGARD framework and/or extend and apply MGARD for various applications, systems, and use cases.

MGARD Foundations

• Qian Gong et al. MGARD: A multigrid framework for high-performance, error-controlled data compression and refactoring. SoftwareX, Dec. 2023
• Xin Liang et al. MGARD+: Optimizing Multilevel Methods for Error-bounded Scientific Data Reduction. IEEE TC, 2021
• Mark Ainsworth et al. Multilevel Techniques for Compression and Reduction of Scientific Data—The Unstructured Case. SIAM Journal on Scientific Computing, 42 (2), A1402–A1427, 2020.
• Mark Ainsworth et al. Multilevel Techniques for Compression and Reduction of Scientific Data—Quantitative Control of Accuracy in Derived Quantities. SIAM Journal on Scientific Computing 41 (4), A2146–A2171, 2019.
• Mark Ainsworth et al. Multilevel Techniques for Compression and Reduction of Scientific Data—The Multivariate Case. SIAM Journal on Scientific Computing 41 (2), A1278–A1303, 2019.
• Mark Ainsworth et al. Multilevel Techniques for Compression and Reduction of Scientific Data—The Univariate Case. Computing and Visualization in Science 19, 65–76, 2018.
• Ben Whitney. Multilevel Techniques for Compression and Reduction of Scientific Data. PhD thesis, Brown University, 2018.

Preserving Quantities of Interest (QoIs)

• Qian Gong et al. Physics-Aware Adaptive Checkpointing with Shadow Systems for Nonlinear PDE Simulations. Journal of Computational Science, Sep. 2026
• Jaemoon Lee et al. Error-Guaranteed Compression with Preservation of Downstream Quantities for Electron Microscopy. Microscopy and Microanalysis, Aug. 2026
• Qian Gong et al. Stability-preserving Lossy Compression for Large-scale Partial Differential Equations. ACM/IEEE SC25, Nov. 2025
• Richard Dodson et al. Optimising the Processing and Storage of Visibilities using lossy compression. Publications of the Astronomical Society of Australia, Jul. 2025
• Qian Gong et al. A General Framework for Error-controlled Unstructured Scientific Data Compression. 2024 e-Science, Sep. 2024
• Tania Banerjee et al. Fast Algorithms for Scientific Data Compression. HiPC, Dec. 2023
• Qian Gong et al. Spatiotemporally adaptive compression for scientific dataset with feature preservation–a case study on simulation data with extreme climate events analysis. 2023 e-Science, Oct. 2023
• Tania Banerjee et al. Online and Scalable Data Compression Pipeline with Guarantees on Quantities of Interest. IEEE e-Science, Oct. 2023
• Tania Banerjee et al. Scalable Hybrid Learning Techniques for Scientific Data Compression., Arxiv, 2022
• Qian Gong et al. Region-adaptive, Error-controlled Scientific Data Compression using Multilevel Decomposition. ACM SSDBM, Jul. 2022
• Tania Benerjee et al. An algorithmic and software pipeline for very large-scale scientific data compression with error guarantees. HiPC, 2022
• Jaemoon Lee et al. Error-bounded learned scientific data compression with preservation of derived quantities. Applied Sciences, 2022
• Qian Gong et al. Maintaining trust in reduction: Preserving the accuracy of quantities of interest for lossy compression. * Smoky Mountains Conference*, Oct. 2021

Progressive Retrieval

• Wenbo Li et al. QProR: An Efficient Framework for Quantity-of-Interest Based Progressive Retrieval with Guaranteed Error Control. ACM HPDC, Jul. 2026
• Yanliang Li et al. HP-MDR: High-performance and Portable Data Refactoring and Progressive Retrieval with Advanced GPUs. ACM/IEEE SC25, Nov 2025
• Xuan Wu et al. Error-controlled Progressive Retrieval of Scientific Data under Derivable Quantities of Interest. ACM/IEEE SC24, Nov. 2024
• Jinzheng Wang et al. Improving Progressive Retrieval for HPC Scientific Data using Deep Neural Network. ICDE, 2023
• Xin Liang et al. Error-controlled, progressive, and adaptable retrieval of scientific data with multilevel decomposition. ACM/IEEE SC21, Nov. 2021

Parallelization and GPU Acceleration

• Yanliang Li et al. BlockMGARD: Accelerating Adaptive Scientific Data Reduction with Region-of-Interest Error Control on GPUs. ACM/IEEE SC26, Nov. 2026
• Jieyang Chen et al. HPDR: High-Performance Portable Scientific Data Reduction Framework. IEEE IPDPS, June. 2025
• Jieyang Chen et al. Scalable Multigrid-based Hierarchical Scientific Data Refactoring on GPUs. Arxiv
• Jieyang Chen et al. Accelerating Multigrid-based Hierarchical Scientific Data Refactoring on GPUs. IEEE IPDPS, May. 2021.

System Optimizations

• Vladislav Esaulov et al. JANUS: Resilient and Adaptive Data Transmission for Enabling Timely and Efficient Cross-Facility Scientific Workflows. ACM HPDC, Jun. 2025
• Lipeng Wan et al. RAPIDS: Reconciling Availability, Accuracy, and Performance in Managing Geo-Distributed Scientific Data. ACM HPDC, Jun. 2023
• Xinying Wang et al. Unbalanced Parallel I/O: An Often-Neglected Side Effect of Lossy Scientific Data Compression. DRBSD-7, Nov. 2021