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Multivariate Scientific Data Compression with Learned Cross-Variable Latent Decorrelation and Autoregressive Entropy Modeling

Liangji Zhu, Anand Rangarajan, Sanjay Ranka

arXiv:2608.30262v1cs.LG

TL;DR

Scientific compressors often fail to model dependence that remains across aligned variables after shared nonlinear encoding. CAESAR-LDAR adds a learned orthogonal latent transform and causal autoregressive prior to a shared CAESAR-V backbone, with common residual correction for error control. Across combustion, climate, and turbulence data, LD helps most when linear latent dependence remains, whereas AR helps with local structure; together they deliver strongest or near-strongest performance across the evaluated datasets.

  • Problem

    Shared scientific compressors often encode variables independently or leave residual aligned-variable dependence unmodeled after nonlinear encoding.

  • Method

    CAESAR-LDAR augments a shared CAESAR-V backbone with latent decorrelation through a learned orthogonal transform and causal autoregressive hierarchical entropy modeling.

  • Results

    At 5 × 10^-4 NRMSE on S3D, CAESAR-LDAR reduces total rate by 43.0% and raises compression ratio by 75.4% over CAESAR-V, while gains differ across datasets.

  • Takeaways & Limitations

    LD is most useful when substantial aligned dependence remains after encoding, while AR applies more broadly to local latent structure despite lower throughput.

  • Takeaways & Limitations

    The method requires dataset-specific training, and one global linear basis cannot capture arbitrary nonlinear or spatially varying relationships.

Abstract

from arXiv · show

Scientific simulations generate collections of physical fields with heterogeneous statistics and dependencies, yet learned compressors often encode those fields independently or rely on a shared encoder without explicitly modeling the structure that remains in latent space. We present CAESAR-LDAR, an error-controlled multivariate learned compressor that augments a shared CAESAR-V backbone with two complementary mechanisms: a trainable orthogonal transform that reorganizes dependence across aligned latent channels, and a causal autoregressive hierarchical prior that captures local spatial structure left after transformation. Orthogonality is maintained through a matrix-exponential parameterization, making the transform exactly invertible without an additional penalty. A common residual-correction stage is applied uniformly to all variants to enforce the requested reconstruction tolerance. Experiments across combustion, climate, and turbulence data show that the two mechanisms are useful in different regimes. Latent decorrelation helps most when substantial linear cross-channel dependence survives the nonlinear encoder, whereas autoregressive modeling remains effective when the remaining structure is primarily local or spatial. Their combination provides the strongest or near-strongest rate-distortion performance across the evaluated datasets. The global transform adds little computational overhead, while autoregressive coding introduces a larger throughput tradeoff. More broadly, the results suggest a practical design principle for multivariate scientific compression: exploit global cross-channel dependence when it is measurably present in latent space, and use local probabilistic context as a complementary mechanism across a wider range of data regimes.

1 INTRODUCTION

The paper targets residual dependence across aligned variables that shared learned encoders leave in latent space. CAESAR-LDAR adds latent decorrelation and autoregressive modeling, whose usefulness varies across application regimes.

  • Shared scientific compression models often exploit within-field redundancy without explicitly modeling dependence remaining across aligned variables.
  • CAESAR-LDAR preserves the shared CAESAR-V backbone while adding a learned orthogonal latent transform and an autoregressive hierarchical prior.The transform addresses aligned latent dependence, while the prior models local spatial context.
  • Error-controlled reconstruction uses a common residual-correction stage applied uniformly across CAESAR-V, LD, AR, and LDAR.The correction stream is added after learned reconstruction to meet the requested tolerance.
  • S3D, E3SM, and JHTDB provide distinct operating regimes: strong LD gains, AR-dominated gains, and smaller gains from both components, respectively.The datasets differ in physics, dimensionality, and channel construction rather than forming a controlled channel-count study.
  • The transform is placed after feature extraction to preserve the shared per-channel encoder and avoid duplicating models for variable groups.
  • The study separates LD and AR contributions through ablations and compares them with variable clustering and a fixed global PCA/KLT basis.

2 RELATED WORK

The paper builds on traditional scientific compressors, learned hyperprior and autoregressive entropy models, and multivariate representations. Its distinguishing choice is to retain a shared nonlinear encoder while adding a global orthogonal transform afterward.

  • Traditional scientific compressors use transforms, prediction, tensor decompositions, or multiresolution representations to exploit structured redundancy.
  • Learned codecs jointly optimize analysis, synthesis, and probability models, with hyperpriors and autoregressive context improving latent entropy modeling.
  • Scientific learned-compression adaptations use architectures such as 3D convolutions, super-resolution, attention, and coordinate-based representations.
  • Existing multivariate methods include tensor decomposition, multilevel reduction, transfer across variables, and joint learned representations.
  • This work preserves a shared per-variable nonlinear encoder and introduces one global orthogonal transform to model residual aligned-channel dependence.
  • Residual correction supplies prescribed error control, with GAE and LBRC selected by the lower valid total rate at each operating point.

3 METHOD

The method encodes aligned blocks with a shared backbone, transforms aligned latent channels, and entropy-codes them using hyperprior and causal spatial context. A post-decoding correction stream enforces the reconstruction tolerance while all representation and coding costs are reported.

  • Aligned-channel architecture: The shared backbone applies the same encoder to aligned variable or variable–plane blocks, forming aligned latent vectors at corresponding features and locations.JHTDB uses G=VD aligned channels by retaining its native spatial planes.
  • Aligned-channel latent transform: Latent decorrelation centers each aligned latent vector and applies a learned orthogonal matrix before quantization, followed by the inverse transform during decoding.
  • Aligned-channel latent transform: Orthogonality is parameterized through a matrix exponential of a skew-symmetric matrix, avoiding an additional orthogonality penalty.The exponential remains orthogonal up to floating-point precision and supports unconstrained optimization.
  • Aligned-channel latent transform: The transform redistributes coordinates without reducing dimensionality, so its success depends on improved quantization and entropy coding rather than discarded components.
  • Autoregressive entropy model: The autoregressive model combines hyperprior features with causal masked-convolution context to predict Gaussian parameters for quantized latent symbols.
  • Autoregressive entropy model: Raster-order coding inserts reconstructed symbols into the context buffer, while LD handles aligned-channel dependence and AR handles within-plane spatial context.
  • Bitstream and reconstruction: The reported rate combines the learned stream with the lower valid GAE or LBRC correction rate selected at each operating point.Zero correction rate is used when learned reconstruction already meets the target, and all four variants use the same rule.

4 EXPERIMENTS

Experiments across combustion, climate, and turbulence datasets show that latent decorrelation and autoregressive modeling provide complementary rate–distortion gains in distinct dependence regimes, with throughput costs concentrated in autoregressive coding.

  • Setup: The evaluation compares CAESAR variants with SZ3 and ZFP at matched achieved macro-NRMSE, using total compressed sizes that include model and correction streams.S3D uses 58 chemical species, E3SM five climate variables, and JHTDB 60 variable–plane channels.
  • Variable Grouping and Fixed PCA: Two clusters improve matched-quality compression by up to about 5%, whereas CAESAR-LD improves compression ratio by roughly 24–53% over shared CAESAR-V.Fixed-PCA improves over the shared model but remains below learned latent decorrelation.
  • S3D Component Ablation: At 5 × 10^-4 NRMSE, LD and AR improve compression ratio over CAESAR-V by 44.1% and 18.9%, while LDAR improves it by 75.4%.At this operating point, LDAR is approximately 5.0× SZ3 and 7.1× ZFP.
  • S3D Component Ablation: LD cuts the primary-latent rate by 51.3%, AR reduces latent and hyperlatent rates by 24.8% and 41.0%, and total rate falls from 0.232 to 0.132 bits/value.The gain narrows at tighter tolerances because residual correction becomes a larger fraction of total rate.
  • Latent Dependence: The learned transform reduces S3D mean absolute off-diagonal latent correlation from 0.5778 to 0.3489, a 39.6% reduction, while primary-latent rate drops from 0.0952 to 0.0464 bits/value.The correlation reduction is distributed across the matrix and follows application of W rather than encoder retraining alone.
  • Latent Dependence: S3D benefits most from LD, E3SM is primarily AR-driven, and JHTDB shows smaller but consistent gains with LDAR strongest over most of the evaluated range.JHTDB’s LD evidence reflects aligned-channel dependence that may combine cross-variable and cross-plane structure.
  • Learned-Codec Runtime: LD adds about 1% throughput overhead, whereas AR reduces throughput by roughly 60%; LDAR closely matches AR.These are learned-codec component throughputs, not end-to-end error-bounded comparisons with SZ3 or ZFP.

5 DISCUSSION

The experiments show that LD and AR benefit different latent regimes, while cross-dataset differences are descriptive rather than causal. Practical selection should use measured latent dependence and total rate, including correction, rather than correlation alone.

  • Mechanism selection: LD is most useful when substantial aligned dependence remains after nonlinear encoding, whereas AR helps when local spatial predictability dominates.E3SM is the low-linear-dependence case where AR contributes more than LD.
  • Regimes: S3D, E3SM, and JHTDB represent distinct operating regimes rather than a controlled channel-count comparison.They differ in physics, dimensionality, and channel construction.
  • Ablation: A classical global basis beats CAESAR-V on S3D, but CAESAR-LD reaches about 398 versus about 315 compression ratio for Fixed-PCA at 5 × 10^-4 NRMSE, a 26.3% advantage.The comparison does not isolate the basis alone because CAESAR-LD adapts jointly while PCA is frozen.
  • Trade-offs: The global transform adds about one percent to learned-codec runtime, while a conditioned or block-adaptive transform would increase computational and bit-accounting complexity.The present global basis is deliberately stored once without block-dependent signaling.
  • Rate accounting: Residual correction must be included in model selection because it can occupy a larger share of total rate at tighter tolerances.The correction backend is fixed across variants and operates after learned reconstruction.
  • Practical configurations: LD alone can suit parallel workflows, whereas AR or LDAR may suit archival storage when additional rate savings justify sequential decoding.LDAR gives the best rate over most of the tested range, but every component need not be used.

6 CONCLUSION AND LIMITATIONS

CAESAR-LDAR extends a shared CAESAR-V codec with latent decorrelation and autoregressive entropy modeling, whose benefits vary across datasets. The results support measuring residual latent dependence before choosing LD, while recognizing throughput, training, and representation-scope limitations.

  • Results: At 5 × 10^-4 NRMSE on S3D, CAESAR-LDAR reduces total rate by 43.0% and raises compression ratio by 75.4% over CAESAR-V.The components were evaluated separately and together across three scientific datasets.
  • Complementarity: LD and AR provide complementary mechanisms: LD targets aligned latent dependence, while AR captures local structure, especially when linear cross-variable dependence is weak.E3SM gains mainly from AR, whereas JHTDB maps three physical fields and 20 planes to 60 aligned channels.
  • Joint learning: A fixed PCA improves on CAESAR-V but remains below the jointly trained CAESAR-LD system.Joint adaptation produces coordinates better suited to quantization and the learned entropy model.
  • Limitations: The global transform is worthwhile only when measurable aligned dependence remains, whereas AR applies more broadly but lowers throughput through sequential coding.The method also requires training for each dataset, and one global linear basis cannot represent arbitrary nonlinear or spatially varying relationships.
  • Error control: Residual correction restores fine-scale information needed by the error bound after the backbone and latent modules model recurring structure and aligned redundancy.The correction stage is common across variants.

A.1 Clustered CAESAR-V

The clustered baseline uses variable descriptors combining coarse spatiotemporal patterns and global statistics, then trains separate CAESAR-V models for groups of similar variables.

  • Descriptor construction: Each variable descriptor combines block-averaged, standardized, PCA-projected field patterns with global and finite-difference statistics.The statistical features include mean, standard deviation, value range, and normalized temporal and spatial finite-difference statistics.
  • Descriptor construction: The descriptor normalizes pattern and statistical feature groups separately before combining them with equal weighting.The group scales are given by their root-mean-square magnitudes.
  • Clustered modeling: K-means partitions the variable descriptors, and a separate CAESAR-V model is trained for each cluster.This tests whether variable-specific specialization recovers structure ignored by one shared CAESAR-V model.
  • Clustered modeling: Blocks remain independently encoded by the model assigned to their physical variable, so the baseline does not jointly encode aligned variables.Cluster-specific model parameters are included in compressed-size accounting.

A.2 Fixed-PCA CAESAR-V

The Fixed-PCA baseline isolates the contribution of a conventional global linear basis by freezing a normally trained CAESAR-V representation and retraining only its entropy-model components.

  • Fixed representation: A CAESAR-V encoder, decoder, super-resolution module, and latent representation are frozen before fitting the fixed basis.The baseline separates conventional global linear-basis effects from end-to-end adaptation.
  • Fixed representation: One global PCA/KLT mean and basis are estimated from training latents with all components retained.The stored mean and basis are included in the compressed-size accounting.
  • Entropy-model retraining: Only the hyper-encoder, hyper-decoder, and entropy prior are retrained around the fixed latent representation.

B CODING, CORRECTION, AND RECONSTRUCTION DETAILS

Each compressed item combines entropy-coded latent streams with model and layout metadata, and LD variants invert their global transform before synthesis.

  • Bitstream contents: A compressed item contains primary-latent and hyperlatent rANS streams, charged model parameters, normalization metadata, tensor dimensions, and aligned-channel layout.LD variants additionally store the global transform and per-sample latent means.
  • Decoding sequence: Decoding restores the hyperlatent first, then the primary latent using either a scale-only or autoregressive prior.
  • Decoding sequence: LD variants apply W⊤ and restore transmitted means before evaluating the shared synthesis network.

B.2 Error-control wrapper

The error-control wrapper accepts a learned operating point only when a residual backend meets the target tolerance, selecting the lower-rate valid correction stream.

  • Tolerance enforcement: The final operating point is accepted only after the residual backend satisfies Eq. (1).
  • Correction selection: GAE and LBRC are evaluated under the same target tolerance, and the lower-rate valid correction stream is selected.
  • Correction selection: If the learned reconstruction already satisfies the target, the correction rate is zero.The reported total includes the learned representation and any sample-specific correction stream.

C JHTDB CHANNEL CONSTRUCTION

The JHTDB setup represents two velocity components and pressure across 20 retained planes, producing 60 aligned variable–plane channels for latent processing.

  • JHTDB uses Cartesian velocity components u_x and u_y together with pressure p on a three-dimensional grid.
  • The shared CAESAR-V backbone processes each input block over time and two in-plane spatial dimensions while retaining 20 planes along the third spatial dimension.
  • The internal channel axis is the Cartesian product of physical variable and retained plane, giving G = 3 × 20 = 60 variable–plane channels.LD operates across this aligned channel axis, while AR operates within each two-dimensional spatial context.
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