Integrating Domain Knowledge in Data-Driven Earth Observation With Process Convolutions

The modelling of Earth observation data is a challenging problem, typically approached by either purely mechanistic or data-driven methods. Mechanistic models encode the domain knowledge and physical rules governing system. Such models, however, need correct specification all interactions between variables in problem appropriate parameterization challenge itself. On other hand, machine learning approaches are flexible tools, able to approximate arbitrarily complex functions, but lack interpretability struggle when scarce extrapolation regimes. In this paper, we argue that hybrid schemes combine both can address these issues efficiently. We introduce Gaussian process (GP) convolution for (EO) problems. specifically propose use class GP called latent force (LFMs) EO time series modelling, analysis understanding. LFMs incorporate encoded differential equations into multioutput model. transfer information across time-series, cope with missing observations, infer explicit functions forcing system, learn parameterizations which very helpful system interpretability. consider soil moisture from active (ASCAT) passive (SMOS, AMSR2) microwave satellites. show how assuming first order equation as equation, model automatically estimates e-folding decay rate related persistence discovers forces precipitation. proposed methodology reconciles two main remote sensing parameter estimation blending statistical modeling.