# Quantile Loss

Ship trajectory forecasting no longer needs recurrent networks or repeated sampling. Earlier AIS-based models either used only the target vessel's history or relied on clustering other vessels, and approximated probability intervals through multiple forward passes. Here the vessel's past positions and a local KDE heat map are fed to a Transformer trained with quantile loss, reaching about 0.18 km average displacement error across three Danish water areas while emitting a prediction interval in a single forward pass.

Ship trajectory forecasting no longer needs recurrent networks or repeated sampling. Earlier AIS-based models either used only the target vessel's history or relied on clustering other vessels, and approximated probability intervals through multiple forward passes. Here the vessel's past positions and a local KDE heat map are fed to a Transformer trained with quantile loss, reaching about 0.18 km average displacement error across three Danish water areas while emitting a prediction interval in a single forward pass.