River meanders are one of the most recurrent and varied patterns in fluvial systems. Multiple attempts have been made to detect and categorise patterns in meandering rivers to understand their shape and evolution. A novel data-driven approach was used to classify single-bend meanders. A dataset containing approximately 10 million single-lobe meander bends was generated using the Kinoshita curve. A neural network autoencoder was trained over the curvature energy spectra of Kinoshita-generated meanders. Then, the trained network was then tested on real meander bends extracted from satellite images, and the energy spectrum in the meander curvature was reconstructed accurately thanks to the autoencoder architecture. The meander spectrum reconstruction was clustered, and three main bend shapes were found associated with the meander datasets, namely symmetric, upstream-skewed, and downstream-skewed. The autoencoder-based classification framework allowed bend shape detection along rivers, finding the dominant pattern with implications on migration trends. By studying the shift in the prevailing bend shape over time, cutoff events were approximately forecast along the Ucayali River, whose migration was remotely sensed for 32 years. Overall, the method proposed opens the venue to data-driven classifications to understand and manage meandering rivers. Bend shape classification can thus inform restoration and flood control practices and contribute to predicting meander evolution from satellite images or sedimentary records.