Large-scale scientific simulations generate massive datasets that pose significant challenges for storage and I/O. While traditional lossy compression techniques can improve performance, balancing compression ratio, data quality, and throughput remains difficult. To address this, we propose NeurLZ, a novel cross-field learning-based and error-controlled compression framework for scientific data. By integrating skipping DNN models, cross-field learning, and error control, our framework aims to substantially enhance lossy compression performance. Our contributions are three-fold: (1) We design a lightweight skipping model to provide high-fidelity detail retention, further improving prediction accuracy. (2) We adopt a cross-field learning approach to significantly improve data prediction accuracy, resulting in a substantially improved compression ratio. (3) We develop an error control approach to provide strict error bounds according to user requirements. We evaluated NeurLZ on several real-world HPC application datasets, including Nyx (cosmological simulation), Miranda (large turbulence simulation), and Hurricane (weather simulation). Experiments demonstrate that our framework achieves up to a 90% relative reduction in bit rate under the same data distortion, compared to the best existing approach.
