# Shape and Time Distortion Loss for Training Deep Time Series Forecasting Models

arXiv: https://arxiv.org/abs/1909.09020 · HTML: https://mlsanity.com/paper/1909.09020/

## Key facts

- Cited by 70 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Sep 2019.

## Built on by (most cited first, 30 of 70)

- [AdaRNN: Adaptive Learning and Forecasting of Time Series](https://mlsanity.com/paper/2108.04443/) (2021)
- [FreDF: Learning to Forecast in the Frequency Domain](https://mlsanity.com/paper/2402.02399/) (2024)
- [HYPRO: A Hybridly Normalized Probabilistic Model for Long-Horizon Prediction of Event Sequences](https://mlsanity.com/paper/2210.01753/) (2022)
- [DBLoss: Decomposition-based Loss Function for Time Series Forecasting](https://mlsanity.com/paper/2510.23672/) (2025)
- [Patch-wise Structural Loss for Time Series Forecasting](https://mlsanity.com/paper/2503.00877/) (2025)
- [GLOBEM Dataset: Multi-Year Datasets for Longitudinal Human Behavior Modeling Generalization](https://mlsanity.com/paper/2211.02733/) (2022)
- [Enhancing Foundation Models for Time Series Forecasting via Wavelet-based Tokenization](https://mlsanity.com/paper/2412.05244/) (2024)
- [Learning Discriminative Prototypes with Dynamic Time Warping](https://mlsanity.com/paper/2103.09458/) (2021)
- [ScanGAN360: A Generative Model of Realistic Scanpaths for 360circ Images](https://mlsanity.com/paper/2103.13922/) (2021)
- [Time-o1: Time-Series Forecasting Needs Transformed Label Alignment](https://mlsanity.com/paper/2505.17847/) (2025)
- [Benchmarking of Deep Learning Irradiance Forecasting Models from Sky Images -- an in-depth Analysis](https://mlsanity.com/paper/2102.00721/) (2021)
- [A Multi-view Multi-task Learning Framework for Multi-variate Time Series Forecasting](https://mlsanity.com/paper/2109.01657/) (2021)
- [Long Horizon Forecasting With Temporal Point Processes](https://mlsanity.com/paper/2101.02815/) (2021)
- [DistDF: Time-Series Forecasting Needs Joint-Distribution Wasserstein Alignment](https://mlsanity.com/paper/2510.24574/) (2025)
- [Deep Time Series Forecasting with Shape and Temporal Criteria](https://mlsanity.com/paper/2104.04610/) (2021)
- [Quadratic Direct Forecast for Training Multi-Step Time-Series Forecast Models](https://mlsanity.com/paper/2511.00053/) (2025)
- [Combating Distribution Shift for Accurate Time Series Forecasting via Hypernetworks](https://mlsanity.com/paper/2202.10808/) (2022)
- [Unsupervised Domain Adaptation for Constraining Star Formation Histories](https://mlsanity.com/paper/2112.14072/) (2021)
- [TILDE-Q: A Transformation Invariant Loss Function for Time-Series Forecasting](https://mlsanity.com/paper/2210.15050/) (2022)
- [Self-Supervised Contrastive Learning for Long-term Forecasting](https://mlsanity.com/paper/2402.02023/) (2024)
- [Selective Learning for Deep Time Series Forecasting](https://mlsanity.com/paper/2510.25207/) (2025)
- [Addressing Prediction Delays in Time Series Forecasting: A Continuous GRU Approach with Derivative Regularization](https://mlsanity.com/paper/2407.01622/) (2024)
- [A Visual Analytics System for Improving Attention-based Traffic Forecasting Models](https://mlsanity.com/paper/2208.04350/) (2022)
- [Modeling Temporal Dependencies within the Target for Long-Term Time Series Forecasting](https://mlsanity.com/paper/2406.04777/) (2024)
- [Deep Declarative Dynamic Time Warping for End-to-End Learning of Alignment Paths](https://mlsanity.com/paper/2303.10778/) (2023)
- [TimeSQL: Improving Multivariate Time Series Forecasting with Multi-Scale Patching and Smooth Quadratic Loss](https://mlsanity.com/paper/2311.11285/) (2023)
- [Vital Sign Forecasting for Sepsis Patients in ICUs](https://mlsanity.com/paper/2311.04770/) (2023)
- [Position: Universal Time Series Foundation Models Rest on a Category Error](https://mlsanity.com/paper/2602.05287/) (2026)
- [Beyond Magnitude and Shape: A Direction-Aware Loss for Time Series Forecasting](https://mlsanity.com/paper/2608.01857/) (2026)
- [Synergetic Learning of Heterogeneous Temporal Sequences for Multi-Horizon Probabilistic Forecasting](https://mlsanity.com/paper/2102.00431/) (2021)

## Abstract (arXiv)

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.