Reconstructing and Forecasting Marine Dynamic Variable Fields across Space and Time Globally and Gaplessly

Abstract: Spatiotemporal projections in marine science are essential for understanding ocean systems and their impact on Earth's climate. However, existing AI-based and statistics-based inversion methods face challenges in leveraging ocean data, generating continuous outputs, and incorporating physical constraints. We propose the Marine Dynamic Reconstruction and Forecast Neural Networks (MDRF-Net), which integrates marine physical mechanisms and observed data to reconstruct and forecast continuous ocean temperature-salinity and dynamic fields. MDRF-Net leverages statistical theories and techniques, incorporating parallel neural network sharing initial layer, two-step training strategy, and ensemble methodology, facilitating in exploring challenging marine areas like the Arctic zone. We have theoretically justified the efficacy of our ensemble method and the rationality of it by providing an upper bound on its generalization error.The effectiveness of MDRF-Net's is validated through a comprehensive simulation study, which highlights its capability to reliably estimate unknown parameters. Comparison with other inversion methods and reanalysis data are also conducted, and the global test error is 0.455{\deg}C for temperature and 0.0714psu for salinity. Overall, MDRF-Net effectively learns the ocean dynamics system using physical mechanisms and statistical insights, contributing to a deeper understanding of marine systems and their impact on the environment and human use of the ocean.