# Deep Time Series Forecasting with Shape and Temporal Criteria

arXiv: https://arxiv.org/abs/2104.04610 · HTML: https://mlsanity.com/paper/2104.04610/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 43 of its 86 references that are in the map.
- First posted on arXiv 9 Apr 2021.

## Builds on (most cited first, 30 of 43)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting](https://mlsanity.com/paper/1506.04214/) (2015)
- [Curiosity-driven Exploration by Self-supervised Prediction](https://mlsanity.com/paper/1705.05363/) (2017)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [N-BEATS: Neural basis expansion analysis for interpretable time series forecasting](https://mlsanity.com/paper/1905.10437/) (2019)
- [Diversity is All You Need: Learning Skills without a Reward Function](https://mlsanity.com/paper/1802.06070/) (2018)
- [Social GAN: Socially Acceptable Trajectories with Generative Adversarial Networks](https://mlsanity.com/paper/1803.10892/) (2018)
- [Enhancing the Locality and Breaking the Memory Bottleneck of Transformer on Time Series Forecasting](https://mlsanity.com/paper/1907.00235/) (2019)
- [A Probabilistic U-Net for Segmentation of Ambiguous Images](https://mlsanity.com/paper/1806.05034/) (2018)
- [Soft-DTW: a Differentiable Loss Function for Time-Series](https://mlsanity.com/paper/1703.01541/) (2017)
- [A Dual-Stage Attention-Based Recurrent Neural Network for Time Series Prediction](https://mlsanity.com/paper/1704.02971/) (2017)
- [Stochastic Variational Video Prediction](https://mlsanity.com/paper/1710.11252/) (2017)
- [A Multi-Horizon Quantile Recurrent Forecaster](https://mlsanity.com/paper/1711.11053/) (2017)
- [Disentangling Physical Dynamics from Unknown Factors for Unsupervised Video Prediction](https://mlsanity.com/paper/2003.01460/) (2020)
- [DLow: Diversifying Latent Flows for Diverse Human Motion Prediction](https://mlsanity.com/paper/2003.08386/) (2020)
- [Think Globally, Act Locally: A Deep Neural Network Approach to High-Dimensional Time Series Forecasting](https://mlsanity.com/paper/1905.03806/) (2019)
- [High-Dimensional Multivariate Forecasting with Low-Rank Gaussian Copula Processes](https://mlsanity.com/paper/1910.03002/) (2019)
- [Multivariate Probabilistic Time Series Forecasting via Conditioned Normalizing Flows](https://mlsanity.com/paper/2002.06103/) (2020)
- [Stochastic Latent Residual Video Prediction](https://mlsanity.com/paper/2002.09219/) (2020)
- [Augmenting Physical Models with Deep Networks for Complex Dynamics Forecasting](https://mlsanity.com/paper/2010.04456/) (2020)
- [Diverse Trajectory Forecasting with Determinantal Point Processes](https://mlsanity.com/paper/1907.04967/) (2019)
- [Shape and Time Distortion Loss for Training Deep Time Series Forecasting Models](https://mlsanity.com/paper/1909.09020/) (2019)
- [Differentiable Dynamic Programming for Structured Prediction and Attention](https://mlsanity.com/paper/1802.03676/) (2018)
- [Deep and Confident Prediction for Time Series at Uber](https://mlsanity.com/paper/1709.01907/) (2017)
- [Analyzing the Variety Loss in the Context of Probabilistic Trajectory Prediction](https://mlsanity.com/paper/1907.10178/) (2019)
- [Differentiable Divergences Between Time Series](https://mlsanity.com/paper/2010.08354/) (2020)

## Built on by (most cited first, 10 of 10)

- [Unsupervised Domain Adaptation for Constraining Star Formation Histories](https://mlsanity.com/paper/2112.14072/) (2021)
- [TimeGNN: Temporal Dynamic Graph Learning for Time Series Forecasting](https://mlsanity.com/paper/2307.14680/) (2023)
- [Deep Time-series Forecasting Needs Kernelized Moment Balancing](https://mlsanity.com/paper/2602.00717/) (2026)
- [Curricular and Cyclical Loss for Time Series Learning Strategy](https://mlsanity.com/paper/2312.15853/) (2023)
- [Real-time respiratory motion forecasting with online learning of recurrent neural networks for accurate targeting in externally guided radiotherapy](https://mlsanity.com/paper/2403.01607/) (2024)
- [Time Series Forecasting via Semi-Asymmetric Convolutional Architecture with Global Atrous Sliding Window](https://mlsanity.com/paper/2301.13691/) (2023)
- [PhyxMamba: Chaotic System Reconstruction from Short Context Observations with Generative State-Space Models](https://mlsanity.com/paper/2505.23863/) (2025)
- [Error Adjustment Based on Spatiotemporal Correlation Fusion for Traffic Forecasting](https://mlsanity.com/paper/2510.23656/) (2025)
- [From Static Spectra to Operando Infrared Dynamics: Physics Informed Flow Modeling and a Benchmark](https://mlsanity.com/paper/2602.18551/) (2026)
- [Deep Time-Series Forecasting in 10 Years: A Survey](https://mlsanity.com/paper/2603.19899/) (2026)

## Abstract (arXiv)

This paper addresses the problem of multi-step time series forecasting for non-stationary signals that can present sudden changes. Current state-of-the-art deep learning forecasting methods, often trained with variants of the MSE, lack the ability to provide sharp predictions in deterministic and probabilistic contexts. To handle these challenges, we propose to incorporate shape and temporal criteria in the training objective of deep models. We define shape and temporal similarities and dissimilarities, based on a smooth relaxation of Dynamic Time Warping (DTW) and Temporal Distortion Index (TDI), that enable to build differentiable loss functions and positive semi-definite (PSD) kernels. With these tools, we introduce DILATE (DIstortion Loss including shApe and TimE), a new objective for deterministic forecasting, that explicitly incorporates two terms supporting precise shape and temporal change detection. For probabilistic forecasting, we introduce STRIPE++ (Shape and Time diverRsIty in Probabilistic forEcasting), a framework for providing a set of sharp and diverse forecasts, where the structured shape and time diversity is enforced with a determinantal point process (DPP) diversity loss. Extensive experiments and ablations studies on synthetic and real-world datasets confirm the benefits of leveraging shape and time features in time series forecasting.