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MeLLoC: Lossless Compression with High-order Mechanism Learning
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Proposes MeLLoC, a lossless compressor for scientific floating-point data that learns a 9-point difference operator (PDE mechanism) via least squares, stores boundary data and a sparser source term, and encodes it with classical entropy coders.
Problem
Lossless compression of large-scale scientific floating-point data is hard because high-order information and roundoff/discretization noise ("false precision") limit the compression ratio of existing entropy coders.
Approach
Treat data as samples of a discretized physical field, learn the local difference operator (9-point template) by least squares so that the residual source term is sparse and low-entropy, store only boundary data plus the source term, and reconstruct by solving the linear system with a Fourier-based periodic-extension solver.
Key results
- MeLLoC achieves 3.36x compression ratio on CESM-ATM, above Zstandard (2.69x) and FPZIP (1.63x).
- On Hurricane, MeLLoC achieves 3.29x compression ratio versus 2.78x for Zstandard.
- MeLLoC throughput is about 189 MB/s compression and 180 MB/s decompression on CESM-ATM, lower than Zstandard's decompression speed (152.81 MB/s is lower too, but Blosc and ALP are much faster in decompression).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use MeLLoC instead of Zstandard | Scientific floating-point data compression · CESM-ATM | compression ratio: 2.69 × -> 3.36 × | Helped |
| Use MeLLoC instead of Zstandard | Scientific floating-point data compression · Hurricane | compression ratio: 2.78 × -> 3.29× | Helped |
| Use MeLLoC instead of the fastest baseline | Scientific floating-point data compression · CESM-ATM | compression throughput: 293.71 Mb/s -> 188.77 Mb/s | Hurt |
| Use MeLLoC instead of the fastest baseline | Scientific floating-point data compression · Hurricane | compression throughput: 888.65 Mb/s -> 206.80Mb/s | Hurt |
| Use MeLLoC instead of the fastest baseline | Scientific floating-point data compression · CESM-ATM | decompression throughput: 1054.95 Mb/s -> 179.76Mb/s | Hurt |
| Use MeLLoC instead of the fastest baseline | Scientific floating-point data compression · Hurricane | decompression throughput: 6516.29 Mb/s -> 190.35Mb/s | Hurt |
Surprising findings
- Blosc and ALP decompress much faster than MeLLoC (e.g., ALP ~1055 MB/s on CESM-ATM), so MeLLoC is not the fastest method.
Limitations
- Performance depends on how well the assumed local second-order PDE models the data.
- Precision control parameter n requires calibration that may be challenging across diverse datasets.
- Not effective for datasets whose order of magnitude does not fit the assumed physical models.
Experimental setup
Datasets: CESM-ATM Hurricane
Benchmarks: CESM-ATM Hurricane
Metrics: compression ratio compression throughput decompression throughput reconstruction error
Baselines: ALP FPZIP ZFP Blosc Gzip Zstandard
Builds on: near-lossless PDE-based compression (Luo et al.) Finite State Entropy SINDy PINNs
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