Indonesia recently implemented a novel, technology-driven approach for conducting agricultural production surveys, which involves monthly observations at many thousands of strategic locations and automated data logging via a cellular phone application. Data from these comprehensive field surveys offer immense value for advancing remote sensing technology to map crop production across Indonesia, particularly through the development of machine learning approaches to relate survey data with satellite imagery. The objective of this study was to compare different machine learning scenarios for classifying and mapping the temporal progression of paddy rice production stages across West Java, Indonesia using synthetic aperture radar (SAR) and optical remote sensing data from Sentinel-1 and Sentinel-2 satellites. Monthly paddy rice survey data at 21,696 locations across West Java from November 2018 through April 2019 were used for model training and testing. Five classes related to rice production stage or other field conditions were defined, including rice at tillering, heading, and harvest stages, rice fields with little to no vegetation present, and non-rice areas. A recurrent neural network (RNN) with long short term memory (LSTM) nodes provided optimal performance with classification accuracies of 79.6% and 75.9% for model training and testing, respectively, and reduced computational effort. Other approaches that incorporated a convolutional neural network (CNN) either reduced classification accuracy or increased computational effort. Deep machine learning methods (RNN and CNN) generally outperformed other non-deep classifiers, which achieved up to 63.3% accuracy for model testing. Classification accuracies were optimized by inputting two Sentinel-1 channels (VH and VV polarizations) and ten Sentinel-2 channels. Temporal patterns of paddy rice production stages were consistent between the monthly ground-based agricultural survey data and 10-m, satellite-based rice classification maps obtained by applying the LSTM-based RNN across West Java. The results demonstrated the value of combining modern agricultural survey data, satellite remote sensing, and a recurrent neural network to develop multitemporal maps of paddy rice production stages.