# Dynamic Modes as Time Representation for Spatiotemporal Forecasting

arXiv: https://arxiv.org/abs/2506.01212 · HTML: https://mlsanity.com/paper/2506.01212/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 45 references that are in the map.
- First posted on arXiv 1 Jun 2025.

## Builds on (most cited first, 18 of 18)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [Multi-Scale Context Aggregation by Dilated Convolutions](https://mlsanity.com/paper/1511.07122/) (2015)
- [Graph WaveNet for Deep Spatial-Temporal Graph Modeling](https://mlsanity.com/paper/1906.00121/) (2019)
- [N-BEATS: Neural basis expansion analysis for interpretable time series forecasting](https://mlsanity.com/paper/1905.10437/) (2019)
- [Adaptive Graph Convolutional Recurrent Network for Traffic Forecasting](https://mlsanity.com/paper/2007.02842/) (2020)
- [GMAN: A Graph Multi-Attention Network for Traffic Prediction](https://mlsanity.com/paper/1911.08415/) (2019)
- [Time2Vec: Learning a Vector Representation of Time](https://mlsanity.com/paper/1907.05321/) (2019)
- [Learnable Fourier Features for Multi-Dimensional Spatial Positional Encoding](https://mlsanity.com/paper/2106.02795/) (2021)
- [Extracting spatial-temporal coherent patterns in large-scale neural recordings using dynamic mode decomposition](https://mlsanity.com/paper/1409.5496/) (2014)
- [Long-Range Transformers for Dynamic Spatiotemporal Forecasting](https://mlsanity.com/paper/2109.12218/) (2021)
- [Sparsity-promoting dynamic mode decomposition](https://mlsanity.com/paper/1309.4165/) (2013)
- [FC-GAGA: Fully Connected Gated Graph Architecture for Spatio-Temporal Traffic Forecasting](https://mlsanity.com/paper/2007.15531/) (2020)

## Built on by (most cited first, 1 of 1)

- [Frequency-Constrained Learning for Long-Term Forecasting](https://mlsanity.com/paper/2508.01508/) (2025)

## Abstract (arXiv)

This paper introduces a data-driven time embedding method for modeling long-range seasonal dependencies in spatiotemporal forecasting tasks. The proposed approach employs Dynamic Mode Decomposition (DMD) to extract temporal modes directly from observed data, eliminating the need for explicit timestamps or hand-crafted time features. These temporal modes serve as time representations that can be seamlessly integrated into deep spatiotemporal forecasting models. Unlike conventional embeddings such as time-of-day indicators or sinusoidal functions, our method captures complex multi-scale periodicity through spectral analysis of spatiotemporal data. Extensive experiments on urban mobility, highway traffic, and climate datasets demonstrate that the DMD-based embedding consistently improves long-horizon forecasting accuracy, reduces residual correlation, and enhances temporal generalization. The method is lightweight, model-agnostic, and compatible with any architecture that incorporates time covariates.