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Abstract Motivation As genomic data becomes more abundant, efficient algorithms and data structures for sequence alignment become increasingly important. The suffix array is a widely used data structure to accelerate alignment, but the binary search algorithm used to query, it requires widespread memory accesses, causing a large number of cache misses on large datasets. Results Here, we present Sapling, an algorithm for sequence alignment, which uses a learned data model to augment the suffix array and enable faster queries. We investigate different types of data models, providing an analysis of different neural network models as well as providing an open-source aligner with a compact, practical piecewise linear model. We show that Sapling outperforms both an optimized binary search approach and multiple widely used read aligners on a diverse collection of genomes, including human, bacteria and plants, speeding up the algorithm by more than a factor of two while adding <1% to the suffix array’s memory footprint. Availability and implementation The source code and tutorial are available open-source at https://github.com/mkirsche/sapling. Supplementary information Supplementary data are available at Bioinformatics online.