EVOLVE: Efficient Learned Volume Compression with Variable-Rate Encoding on a Cross-Domain Database

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.

Recent work has shown that implicit neural representations (INRs) can be trained to effectively compress structured and unstructured volume data, allowing for direct data querying with a reduced memory footprint. However, as existing INRs for unstructured volumes do not encode geometry, they require partial mesh storage for later sampling, limiting achievable compression. At the same time, novel view synthesis methods have shown that explicit collections of 3D Gaussians can be used to accurately visualize volume data. In this work, we introduce an explicit model for volume data compression based on 3D Gaussian primitives. We reinterpret collections of 3D Gaussians as an explicit representation of a scalar field and use a sampling strategy that reconstructs scalar values at spatial locations through weighted aggregation of intersecting Gaussians. We develop optimized CUDA-accelerated pipelines for structured and unstructured model sampling, loss functions that encourage accurate domain encoding by our models, and a novel sampling-error based densification strategy. Our explicit formulation naturally encodes domain geometry, eliminating the need for mesh storage in unstructured volumes and introducing significantly higher compression opportunities. Compared to existing INRs, we demonstrate that our explicit model achieves competitive reconstruction quality with significant training speedups on structured volumes, while markedly outperforming in all metrics on unstructured volumes.

Lossy compression is essential for massive spatiotemporal data from scientific simulations. Learned compressors can achieve high compression ratios at moderate accuracy targets, but their aggregate reconstruction losses do not guarantee accuracy for each block. Existing Guaranteed Autoencoder (GAE) methods add a per-block residual correction by retaining SVD/PCA-style coefficients until the target is met. This works at moderate tolerances, but in the high-fidelity regime with block-level NRMSE from 10^-6 to 10^-4, the number of retained coefficients grows quickly and the correction stream dominates the total rate. We propose a residual-centric view: the learned residual is structurally different from the original scientific field and should be coded with a representation designed for that residual. We introduce two residual coders. LBRC is a deterministic, training-free pipeline that adaptively quantizes the learned residual to the target NRMSE and losslessly encodes the resulting integer residual using 3D Lorenzo differencing, zigzag mapping, bit-plane coding, and entropy coding. NGLR adds a causal neural predictor that outputs a normalized bias for an integer-rounded Lorenzo prediction in the same deterministic integer pipeline, reducing the entropy of the remaining residual code while preserving deterministic decoding. The predictor weights are serialized and counted in the bitstream. Across E3SM, JHTDB, and ERA5 at block-level NRMSE targets from 10^-6 to 10^-4, LBRC improves compression ratio over GAE by 30-60% and is broadly competitive with SZ. NGLR adds a further 10-40% over LBRC and outperforms SZ in the evaluated high-fidelity regime. These results show that residual representations tailored to learned-compressor residuals can preserve the advantage of learned compression when global residual correction becomes rate-dominant.