  This paper addresses the problem of time series forecasting for
non-stationary signals and multiple future steps prediction. To handle this
challenging task, we introduce DILATE (DIstortion Loss including shApe and
TimE), a new objective function for training deep neural networks. DILATE aims
at accurately predicting sudden changes, and explicitly incorporates two terms
supporting precise shape and temporal change detection. We introduce a
differentiable loss function suitable for training deep neural nets, and
provide a custom back-prop implementation for speeding up optimization. We also
introduce a variant of DILATE, which provides a smooth generalization of
temporally-constrained Dynamic Time Warping (DTW). Experiments carried out on
various non-stationary datasets reveal the very good behaviour of DILATE
compared to models trained with the standard Mean Squared Error (MSE) loss
function, and also to DTW and variants. DILATE is also agnostic to the choice
of the model, and we highlight its benefit for training fully connected
networks as well as specialized recurrent architectures, showing its capacity
to improve over state-of-the-art trajectory forecasting approaches.
