# Urban traffic analysis and forecasting through shared Koopman eigenmodes

arXiv: https://arxiv.org/abs/2409.04728 · HTML: https://mlsanity.com/paper/2409.04728/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 143 references that are in the map.
- First posted on arXiv 7 Sep 2024.

## Builds on (most cited first, 19 of 19)

- [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)
- [Large Language Models Are Zero-Shot Time Series Forecasters](https://mlsanity.com/paper/2310.07820/) (2023)
- [ForecastPFN: Synthetically-Trained Zero-Shot Forecasting](https://mlsanity.com/paper/2311.01933/) (2023)
- [Language Models Still Struggle to Zero-shot Reason about Time Series](https://mlsanity.com/paper/2404.11757/) (2024)
- [Meta-learning framework with applications to zero-shot time-series forecasting](https://mlsanity.com/paper/2002.02887/) (2020)
- [Learning from Multiple Cities: A Meta-Learning Approach for Spatial-Temporal Prediction](https://mlsanity.com/paper/1901.08518/) (2019)
- [Cross-city Few-Shot Traffic Forecasting via Traffic Pattern Bank](https://mlsanity.com/paper/2308.09727/) (2023)
- [Fourier neural operator for learning solutions to macroscopic traffic flow models: Application to the forward and inverse problems](https://mlsanity.com/paper/2308.07051/) (2023)
- [Incorporating Kinematic Wave Theory into a Deep Learning Method for High-Resolution Traffic Speed Estimation](https://mlsanity.com/paper/2102.02906/) (2021)
- [Nonlinear Traffic Prediction as a Matrix Completion Problem with Ensemble Learning](https://mlsanity.com/paper/2001.02492/) (2020)
- [Learning-based solutions to nonlinear hyperbolic PDEs: Empirical insights on generalization errors](https://mlsanity.com/paper/2302.08144/) (2023)
- [Discovering Dynamic Patterns from Spatiotemporal Data with Time-Varying Low-Rank Autoregression](https://mlsanity.com/paper/2211.15482/) (2022)
- [Traffic Prediction with Transfer Learning: A Mutual Information-based Approach](https://mlsanity.com/paper/2303.07184/) (2023)
- [Multi-scale Perimeter Control Approach in a Connected-Vehicle Environment](https://mlsanity.com/paper/1612.05910/) (2016)
- [Traffic state estimation using stochastic Lagrangian dynamics](https://mlsanity.com/paper/1806.02692/) (2018)
- [Learning Traffic Speed Dynamics from Visualizations](https://mlsanity.com/paper/2105.01423/) (2021)
- [Generalized adaptive smoothing based neural network architecture for traffic state estimation](https://mlsanity.com/paper/2301.03439/) (2023)
- [A dynamic multi-region MFD model for ride-sourcing with ridesplitting](https://mlsanity.com/paper/2211.14560/) (2022)

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

- [Catastrophic Overfitting, Entropy Gap and Participation Ratio: A Noiseless lp Norm Solution for Fast Adversarial Training](https://mlsanity.com/paper/2505.02360/) (2025)
- [FlowMixer: A Depth-Agnostic Neural Architecture for Interpretable Spatiotemporal Forecasting](https://mlsanity.com/paper/2505.16786/) (2025)
- [Learning to Learn the Macroscopic Fundamental Diagram using Physics-Informed and meta Machine Learning techniques](https://mlsanity.com/paper/2508.14137/) (2025)
- [Fractional is Better: Learnable Derivative Orders in Neural Operator Learning](https://mlsanity.com/paper/2610.20363/) (2026)

## Abstract (arXiv)

Predicting traffic flow in data-scarce cities is challenging due to limited historical data. To address this, we leverage transfer learning by identifying periodic patterns common to data-rich cities using a customized variant of Dynamic Mode Decomposition (DMD): constrained Hankelized DMD (TrHDMD). This method uncovers common eigenmodes (urban heartbeats) in traffic patterns and transfers them to data-scarce cities, significantly enhancing prediction performance. TrHDMD reduces the need for extensive training datasets by utilizing prior knowledge from other cities. By applying Koopman operator theory to multi-city loop detector data, we identify stable, interpretable, and time-invariant traffic modes. Injecting ``urban heartbeats'' into forecasting tasks improves prediction accuracy and has the potential to enhance traffic management strategies for cities with varying data infrastructures. Our work introduces cross-city knowledge transfer via shared Koopman eigenmodes, offering actionable insights and reliable forecasts for data-scarce urban environments.