# Monotonic Neural Ordinary Differential Equation: Time-series Forecasting for Cumulative Data

arXiv: https://arxiv.org/abs/2309.13452 · HTML: https://mlsanity.com/paper/2309.13452/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 23 references that are in the map.
- First posted on arXiv 23 Sep 2023.

## Builds on (most cited first, 13 of 13)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [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)
- [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)
- [An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling](https://mlsanity.com/paper/1803.01271/) (2018)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [Enhancing the Locality and Breaking the Memory Bottleneck of Transformer on Time Series Forecasting](https://mlsanity.com/paper/1907.00235/) (2019)
- [Recurrent Neural Networks for Multivariate Time Series with Missing Values](https://mlsanity.com/paper/1606.01865/) (2016)
- [Neural Controlled Differential Equations for Irregular Time Series](https://mlsanity.com/paper/2005.08926/) (2020)
- [Transformers in Time Series: A Survey](https://mlsanity.com/paper/2202.07125/) (2022)

## Built on by (most cited first, 9 of 9)

- [DUET: Dual Clustering Enhanced Multivariate Time Series Forecasting](https://mlsanity.com/paper/2412.10859/) (2024)
- [Time-o1: Time-Series Forecasting Needs Transformed Label Alignment](https://mlsanity.com/paper/2505.17847/) (2025)
- [DistDF: Time-Series Forecasting Needs Joint-Distribution Wasserstein Alignment](https://mlsanity.com/paper/2510.24574/) (2025)
- [Quadratic Direct Forecast for Training Multi-Step Time-Series Forecast Models](https://mlsanity.com/paper/2511.00053/) (2025)
- [K2VAE: A Koopman-Kalman Enhanced Variational AutoEncoder for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2505.23017/) (2025)
- [Multiscale Representation Enhanced Temporal Flow Fusion Model for Long-Term Workload Forecasting](https://mlsanity.com/paper/2407.19697/) (2024)
- [Deep Time-series Forecasting Needs Kernelized Moment Balancing](https://mlsanity.com/paper/2602.00717/) (2026)
- [Deep Time-Series Forecasting in 10 Years: A Survey](https://mlsanity.com/paper/2603.19899/) (2026)
- [Frequency-Domain Neural ODEs for Modeling Non-Linear Dynamical Systems](https://mlsanity.com/paper/2606.22075/) (2026)

## Abstract (arXiv)

Time-Series Forecasting based on Cumulative Data (TSFCD) is a crucial problem in decision-making across various industrial scenarios. However, existing time-series forecasting methods often overlook two important characteristics of cumulative data, namely monotonicity and irregularity, which limit their practical applicability. To address this limitation, we propose a principled approach called Monotonic neural Ordinary Differential Equation (MODE) within the framework of neural ordinary differential equations. By leveraging MODE, we are able to effectively capture and represent the monotonicity and irregularity in practical cumulative data. Through extensive experiments conducted in a bonus allocation scenario, we demonstrate that MODE outperforms state-of-the-art methods, showcasing its ability to handle both monotonicity and irregularity in cumulative data and delivering superior forecasting performance.