# Long-term Time Series Forecasting based on Decomposition and Neural Ordinary Differential Equations

arXiv: https://arxiv.org/abs/2311.04522 · HTML: https://mlsanity.com/paper/2311.04522/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 50 references that are in the map.
- First posted on arXiv 8 Nov 2023.

## Builds on (most cited first, 30 of 31)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [On the Properties of Neural Machine Translation: Encoder-Decoder Approaches](https://mlsanity.com/paper/1409.1259/) (2014)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [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)
- [Enhancing the Locality and Breaking the Memory Bottleneck of Transformer on Time Series Forecasting](https://mlsanity.com/paper/1907.00235/) (2019)
- [Transformers in Time Series: A Survey](https://mlsanity.com/paper/2202.07125/) (2022)
- [Time Series Forecasting With Deep Learning: A Survey](https://mlsanity.com/paper/2004.13408/) (2020)
- [InceptionTime: Finding AlexNet for Time Series Classification](https://mlsanity.com/paper/1909.04939/) (2019)
- [How to train your neural ODE: the world of Jacobian and kinetic regularization](https://mlsanity.com/paper/2002.02798/) (2020)
- [Adversarial Audio Synthesis](https://mlsanity.com/paper/1802.04208/) (2018)
- [Neural Rough Differential Equations for Long Time Series](https://mlsanity.com/paper/2009.08295/) (2020)
- [Graph Neural Controlled Differential Equations for Traffic Forecasting](https://mlsanity.com/paper/2112.03558/) (2021)
- [GT-GAN: General Purpose Time Series Synthesis with Generative Adversarial Networks](https://mlsanity.com/paper/2210.02040/) (2022)
- [MALI: A memory efficient and reverse accurate integrator for Neural ODEs](https://mlsanity.com/paper/2102.04668/) (2021)
- [Koopman Neural Forecaster for Time Series with Temporal Distribution Shifts](https://mlsanity.com/paper/2210.03675/) (2022)
- [Attentive Neural Controlled Differential Equations for Time-series Classification and Forecasting](https://mlsanity.com/paper/2109.01876/) (2021)
- [DEPTS: Deep Expansion Learning for Periodic Time Series Forecasting](https://mlsanity.com/paper/2203.07681/) (2022)
- [EXIT: Extrapolation and Interpolation-based Neural Controlled Differential Equations for Time-series Classification and Forecasting](https://mlsanity.com/paper/2204.08771/) (2022)
- [Climate Modeling with Neural Diffusion Equations](https://mlsanity.com/paper/2111.06011/) (2021)
- [ACE-NODE: Attentive Co-Evolving Neural Ordinary Differential Equations](https://mlsanity.com/paper/2105.14953/) (2021)
- [Graph Neural Rough Differential Equations for Traffic Forecasting](https://mlsanity.com/paper/2303.10909/) (2023)
- [LightMove: A Lightweight Next-POI Recommendation for Taxicab Rooftop Advertising](https://mlsanity.com/paper/2108.04993/) (2021)
- [Learnable Path in Neural Controlled Differential Equations](https://mlsanity.com/paper/2301.04333/) (2023)
- [TimeKit: A Time-series Forecasting-based Upgrade Kit for Collaborative Filtering](https://mlsanity.com/paper/2211.04266/) (2022)
- [LORD: Lower-Dimensional Embedding of Log-Signature in Neural Rough Differential Equations](https://mlsanity.com/paper/2204.08781/) (2022)

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

- [Quantum-Optimized Selective State Space Model for Efficient Time Series Prediction](https://mlsanity.com/paper/2509.00259/) (2025)

## Abstract (arXiv)

Long-term time series forecasting (LTSF) is a challenging task that has been investigated in various domains such as finance investment, health care, traffic, and weather forecasting. In recent years, Linear-based LTSF models showed better performance, pointing out the problem of Transformer-based approaches causing temporal information loss. However, Linear-based approach has also limitations that the model is too simple to comprehensively exploit the characteristics of the dataset. To solve these limitations, we propose LTSF-DNODE, which applies a model based on linear ordinary differential equations (ODEs) and a time series decomposition method according to data statistical characteristics. We show that LTSF-DNODE outperforms the baselines on various real-world datasets. In addition, for each dataset, we explore the impacts of regularization in the neural ordinary differential equation (NODE) framework.