  The forecasting and reconstruction of ocean and atmosphere dynamics from
satellite observation time series are key challenges. While model-driven
representations remain the classic approaches, data-driven representations
become more and more appealing to benefit from available large-scale
observation and simulation datasets. In this work we investigate the relevance
of recently introduced bilinear residual neural network representations, which
mimic numerical integration schemes such as Runge-Kutta, for the forecasting
and assimilation of geophysical fields from satellite-derived remote sensing
data. As a case-study, we consider satellite-derived Sea Surface Temperature
time series off South Africa, which involves intense and complex upper ocean
dynamics. Our numerical experiments demonstrate that the proposed patch-level
neural-network-based representations outperform other data-driven models,
including analog schemes, both in terms of forecasting and missing data
interpolation performance with a relative gain up to 50\% for highly dynamic
areas.
