# DualDynamics: Synergizing Implicit and Explicit Methods for Robust Irregular Time Series Analysis

arXiv: https://arxiv.org/abs/2401.04979 · HTML: https://mlsanity.com/paper/2401.04979/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 62 references that are in the map.
- First posted on arXiv 10 Jan 2024.

## Builds on (most cited first, 30 of 42)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [DeepMind Control Suite](https://mlsanity.com/paper/1801.00690/) (2018)
- [FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models](https://mlsanity.com/paper/1810.01367/) (2018)
- [Recurrent Neural Networks for Multivariate Time Series with Missing Values](https://mlsanity.com/paper/1606.01865/) (2016)
- [Ray: A Distributed Framework for Emerging AI Applications](https://mlsanity.com/paper/1712.05889/) (2017)
- [Temporal Convolutional Networks for Action Segmentation and Detection](https://mlsanity.com/paper/1611.05267/) (2016)
- [Neural Controlled Differential Equations for Irregular Time Series](https://mlsanity.com/paper/2005.08926/) (2020)
- [The UCR Time Series Archive](https://mlsanity.com/paper/1810.07758/) (2018)
- [Augmented Neural ODEs](https://mlsanity.com/paper/1904.01681/) (2019)
- [Tune: A Research Platform for Distributed Model Selection and Training](https://mlsanity.com/paper/1807.05118/) (2018)
- [Invertible Residual Networks](https://mlsanity.com/paper/1811.00995/) (2018)
- [The UEA multivariate time series classification archive, 2018](https://mlsanity.com/paper/1811.00075/) (2018)
- [Scalable Gradients for Stochastic Differential Equations](https://mlsanity.com/paper/2001.01328/) (2020)
- [Multi-Time Attention Networks for Irregularly Sampled Time Series](https://mlsanity.com/paper/2101.10318/) (2021)
- [GRU-ODE-Bayes: Continuous modeling of sporadically-observed time series](https://mlsanity.com/paper/1905.12374/) (2019)
- [Doctor AI: Predicting Clinical Events via Recurrent Neural Networks](https://mlsanity.com/paper/1511.05942/) (2015)
- [Beyond Finite Layer Neural Networks: Bridging Deep Architectures and Numerical Differential Equations](https://mlsanity.com/paper/1710.10121/) (2017)
- [Dissecting Neural ODEs](https://mlsanity.com/paper/2002.08071/) (2020)
- [Neural Jump Stochastic Differential Equations](https://mlsanity.com/paper/1905.10403/) (2019)
- [OT-Flow: Fast and Accurate Continuous Normalizing Flows via Optimal Transport](https://mlsanity.com/paper/2006.00104/) (2020)
- [Neural Rough Differential Equations for Long Time Series](https://mlsanity.com/paper/2009.08295/) (2020)
- [sktime: A Unified Interface for Machine Learning with Time Series](https://mlsanity.com/paper/1909.07872/) (2019)
- [Neural Flows: Efficient Alternative to Neural ODEs](https://mlsanity.com/paper/2110.13040/) (2021)

## Built on by (most cited first, 4 of 4)

- [Comprehensive Review of Neural Differential Equations for Time Series Analysis](https://mlsanity.com/paper/2502.09885/) (2025)
- [One-Step Graph-Structured Neural Flows for Irregular Multivariate Time Series Classification](https://mlsanity.com/paper/2605.10179/) (2026)
- [Function-Space Priors for Bayesian Neural ODEs with Application to Vessel Trajectory Prediction](https://mlsanity.com/paper/2606.06351/) (2026)
- [Rarity-Gated Context Conditioning for Offline Imitation Learning-Based Maritime Anomaly Detection](https://mlsanity.com/paper/2606.13311/) (2026)

## Abstract (arXiv)

Real-world time series analysis faces significant challenges when dealing with irregular and incomplete data. While Neural Differential Equation (NDE) based methods have shown promise, they struggle with limited expressiveness, scalability issues, and stability concerns. Conversely, Neural Flows offer stability but falter with irregular data. We introduce 'DualDynamics', a novel framework that synergistically combines NDE-based method and Neural Flow-based method. This approach enhances expressive power while balancing computational demands, addressing critical limitations of existing techniques. We demonstrate DualDynamics' effectiveness across diverse tasks: classification of robustness to dataset shift, irregularly-sampled series analysis, interpolation of missing data, and forecasting with partial observations. Our results show consistent outperformance over state-of-the-art methods, indicating DualDynamics' potential to advance irregular time series analysis significantly.