# RNN with Particle Flow for Probabilistic Spatio-temporal Forecasting

arXiv: https://arxiv.org/abs/2106.06064 · HTML: https://mlsanity.com/paper/2106.06064/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 45 of its 86 references that are in the map.
- First posted on arXiv 10 Jun 2021.

## Builds on (most cited first, 30 of 45)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [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)
- [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)
- [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)
- [Graph WaveNet for Deep Spatial-Temporal Graph Modeling](https://mlsanity.com/paper/1906.00121/) (2019)
- [Scheduled Sampling for Sequence Prediction with Recurrent Neural Networks](https://mlsanity.com/paper/1506.03099/) (2015)
- [N-BEATS: Neural basis expansion analysis for interpretable time series forecasting](https://mlsanity.com/paper/1905.10437/) (2019)
- [Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks](https://mlsanity.com/paper/2005.11650/) (2020)
- [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)
- [A Recurrent Latent Variable Model for Sequential Data](https://mlsanity.com/paper/1506.02216/) (2015)
- [A Dual-Stage Attention-Based Recurrent Neural Network for Time Series Prediction](https://mlsanity.com/paper/1704.02971/) (2017)
- [A Multi-Horizon Quantile Recurrent Forecaster](https://mlsanity.com/paper/1711.11053/) (2017)
- [Spatial-Temporal Transformer Networks for Traffic Flow Forecasting](https://mlsanity.com/paper/2001.02908/) (2020)
- [Think Globally, Act Locally: A Deep Neural Network Approach to High-Dimensional Time Series Forecasting](https://mlsanity.com/paper/1905.03806/) (2019)
- [Deep Variational Bayes Filters: Unsupervised Learning of State Space Models from Raw Data](https://mlsanity.com/paper/1605.06432/) (2016)
- [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)
- [Sequential Neural Models with Stochastic Layers](https://mlsanity.com/paper/1605.07571/) (2016)
- [A Disentangled Recognition and Nonlinear Dynamics Model for Unsupervised Learning](https://mlsanity.com/paper/1710.05741/) (2017)
- [Variational Sequential Monte Carlo](https://mlsanity.com/paper/1705.11140/) (2017)
- [Filtering Variational Objectives](https://mlsanity.com/paper/1705.09279/) (2017)
- [Deep Factors for Forecasting](https://mlsanity.com/paper/1905.12417/) (2019)
- [Multi-Range Attentive Bicomponent Graph Convolutional Network for Traffic Forecasting](https://mlsanity.com/paper/1911.12093/) (2019)
- [Auto-Encoding Sequential Monte Carlo](https://mlsanity.com/paper/1705.10306/) (2017)
- [Particle Filter Networks with Application to Visual Localization](https://mlsanity.com/paper/1805.08975/) (2018)

## Built on by (most cited first, 16 of 16)

- [DiffSTG: Probabilistic Spatio-Temporal Graph Forecasting with Denoising Diffusion Models](https://mlsanity.com/paper/2301.13629/) (2023)
- [Graph Deep Learning for Time Series Forecasting](https://mlsanity.com/paper/2310.15978/) (2023)
- [Relational Conformal Prediction for Correlated Time Series](https://mlsanity.com/paper/2502.09443/) (2025)
- [Taming the Long Tail of Deep Probabilistic Forecasting](https://mlsanity.com/paper/2202.13418/) (2022)
- [Cheap and Deterministic Inference for Deep State-Space Models of Interacting Dynamical Systems](https://mlsanity.com/paper/2305.01773/) (2023)
- [SpecSTG: A Fast Spectral Diffusion Framework for Probabilistic Spatio-Temporal Traffic Forecasting](https://mlsanity.com/paper/2401.08119/) (2024)
- [OXYGENERATOR: Reconstructing Global Ocean Deoxygenation Over a Century with Deep Learning](https://mlsanity.com/paper/2405.07233/) (2024)
- [Graph State-Space Models and Latent Relational Inference](https://mlsanity.com/paper/2301.01741/) (2023)
- [Assessment of Spatio-Temporal Predictors in the Presence of Missing and Heterogeneous Data](https://mlsanity.com/paper/2302.01701/) (2023)
- [Learning Energy-Based Generative Models via Potential Flow: A Variational Principle Approach to Probability Density Homotopy Matching](https://mlsanity.com/paper/2504.16262/) (2025)
- [Learning Mixture Structure on Multi-Source Time Series for Probabilistic Forecasting](https://mlsanity.com/paper/2302.11078/) (2023)
- [LINOCS: Lookahead Inference of Networked Operators for Continuous Stability](https://mlsanity.com/paper/2404.18267/) (2024)
- [Sub-Graph Learning for Spatiotemporal Forecasting via Knowledge Distillation](https://mlsanity.com/paper/2211.09740/) (2022)
- [Variational Potential Flow: A Novel Probabilistic Framework for Energy-Based Generative Modelling](https://mlsanity.com/paper/2407.15238/) (2024)
- [Denoising Refinement Diffusion Models for Simultaneous Generation of Multi-scale Mobile Network Traffic](https://mlsanity.com/paper/2511.17532/) (2025)
- [Addressing Spatial Indistinguishability in Spatiotemporal Prediction via Optimal Transport-Guided Masking](https://mlsanity.com/paper/2609.35021/) (2026)

## Abstract (arXiv)

Spatio-temporal forecasting has numerous applications in analyzing wireless, traffic, and financial networks. Many classical statistical models often fall short in handling the complexity and high non-linearity present in time-series data. Recent advances in deep learning allow for better modelling of spatial and temporal dependencies. While most of these models focus on obtaining accurate point forecasts, they do not characterize the prediction uncertainty. In this work, we consider the time-series data as a random realization from a nonlinear state-space model and target Bayesian inference of the hidden states for probabilistic forecasting. We use particle flow as the tool for approximating the posterior distribution of the states, as it is shown to be highly effective in complex, high-dimensional settings. Thorough experimentation on several real world time-series datasets demonstrates that our approach provides better characterization of uncertainty while maintaining comparable accuracy to the state-of-the art point forecasting methods.