Neural Residual Modeling for Scientific Data Compression under Guaranteed Error Bounds

Lossy compression of scientific simulation data increasingly relies on learned, latent-space architectures such as Residual Vector Quantization (RVQ), which iteratively quantize a base representation and its residuals to progressively reduce reconstruction error. While effective, RVQ performs this residual modeling entirely in latent space, leaving the pixel-space error structure of the reconstruction largely unaddressed. In this work, we propose a post-processing pipeline that augments an RVQ-based compressor with a U-Net trained to predict and correct pixel-space residuals between the original volume and its RVQ reconstruction. We show that these residuals are spatially structured rather than driven by local intensity or gradient features, motivating the need for a deep spatial model rather than simple statistical correction. The U-Net-corrected reconstruction is then passed through a Guaranteed Autoencoder (GAE) stage, which projects the remaining residual onto a per-block PCA basis to enforce a user-specified block-wise error bound. To the best of our knowledge, this is the first pipeline to combine latent-space RVQ, explicit pixel-space residual correction via a deep spatial post-processing network, and GAE-based error-bound guarantees within a single framework for scientific data compression. We evaluate our approach on S3D, JHTDB and E3SM datasets, demonstrating consistent improvements in NRMSE, compression ratio] over RVQ-only and standard residual-correction baselines, while maintaining strict error guarantees required for scientific data fidelity.