  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.
