Improving Global Sea Level Prediction with Hard Physical Constraints in Neural Networks

Incorporating physical laws into neural networks has long been a central topic in geophysical machine learning. While purely data-driven approaches can achieve strong prediction skill, they often lack physical consistency and degrade under sparse observations or long lead times. In this study, we impose a simple yet fundamental constraint, global volume conservation, by introducing a dedicated volume-conserving layer into neural networks. We apply this volume-conserved network in both an idealized shallow-water model and a realistic global sea level anomaly prediction task, and show systematic improvements in prediction skill, reaching up to 25%. The improvement increases as observation points decreasing and leading time increasing, and the predictions follow physical laws strictly. In addition, although post-processing also enforce physical consistency, the constrained model achieves substantially lower prediction errors, with reductions of up to 15%. These results demonstrate the effectiveness of embedding hard physical constraints as network layers for improving both accuracy and physical fidelity.