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Satellite remote sensing has now become a unique tool for continuous and predictable monitoring of geosystems at various scales, observing the dynamics of different geophysical parameters of the environment. One of the essential problems with most satellite environmental monitoring methods is their sensitivity to atmospheric conditions, in particular cloud cover, which leads to the loss of a significant part of data, especially at high latitudes, potentially reducing the quality of observation time series until it is useless. In this paper, we present a toolbox for filling gaps in remote sensing time-series data based on machine learning algorithms and spatio-temporal statistics. The first implemented procedure allows us to fill gaps based on spatial relationships between pixels, obtained from historical time-series. Then, the second procedure is dedicated to filling the remaining gaps based on the temporal dynamics of each pixel value. The algorithm was tested and verified on Sentinel-3 SLSTR and Terra MODIS land surface temperature data and under different geographical and seasonal conditions. As a result of validation, it was found that in most cases the error did not exceed 1 °C. The algorithm was also verified for gaps restoration in Terra MODIS derived normalized difference vegetation index and land surface broadband albedo datasets. The software implementation is Python-based and distributed under conditions of GNU GPL 3 license via public repository.

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The data-driven models allow one to dene the model structure in cases when a priori information is not sucient to build other types of models. The possible way to obtain physical interpretation is the data-driven differential equation discovery techniques. The existing methods of PDE (partial derivative equations) discovery are bound with the sparse regression. However, sparse regression is restricting the resulting model form, since the terms for PDE are defined before regression. The evolutionary approach described in the article has a symbolic regression as the background instead and thus has fewer restrictions on the PDE form. The evolutionary method of PDE discovery (EPDE) is described and tested on several canonical PDEs. The question of robustness is examined on a noised data example.

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