# Learning Spatio-Temporal Dynamics for Trajectory Recovery via Time-Aware Transformer

arXiv: https://arxiv.org/abs/2505.13857 · HTML: https://mlsanity.com/paper/2505.13857/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 84 references that are in the map.
- First posted on arXiv 20 May 2025.

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

- [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)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [How Attentive are Graph Attention Networks?](https://mlsanity.com/paper/2105.14491/) (2021)
- [Neural Controlled Differential Equations for Irregular Time Series](https://mlsanity.com/paper/2005.08926/) (2020)
- [How Do Vision Transformers Work?](https://mlsanity.com/paper/2202.06709/) (2022)
- [Multi-Time Attention Networks for Irregularly Sampled Time Series](https://mlsanity.com/paper/2101.10318/) (2021)
- [Spatio-Temporal Graph Transformer Networks for Pedestrian Trajectory Prediction](https://mlsanity.com/paper/2005.08514/) (2020)
- [Time2Vec: Learning a Vector Representation of Time](https://mlsanity.com/paper/1907.05321/) (2019)
- [Spatial-Temporal Graph ODE Networks for Traffic Flow Forecasting](https://mlsanity.com/paper/2106.12931/) (2021)
- [Liquid Time-constant Networks](https://mlsanity.com/paper/2006.04439/) (2020)
- [Multivariate Time Series Forecasting with Dynamic Graph Neural ODEs](https://mlsanity.com/paper/2202.08408/) (2022)
- [Closed-form Continuous-time Neural Models](https://mlsanity.com/paper/2106.13898/) (2021)
- [ContiFormer: Continuous-Time Transformer for Irregular Time Series Modeling](https://mlsanity.com/paper/2402.10635/) (2024)
- [Self-supervised Trajectory Representation Learning with Temporal Regularities and Travel Semantics](https://mlsanity.com/paper/2211.09510/) (2022)
- [Contrastive Trajectory Similarity Learning with Dual-Feature Attention](https://mlsanity.com/paper/2210.05155/) (2022)
- [Deep Spatially and Temporally Aware Similarity Computation for Road Network Constrained Trajectories](https://mlsanity.com/paper/2112.09339/) (2021)
- [DeepTravel: a Neural Network Based Travel Time Estimation Model with Auxiliary Supervision](https://mlsanity.com/paper/1802.02147/) (2018)
- [RNTrajRec: Road Network Enhanced Trajectory Recovery with Spatial-Temporal Transformer](https://mlsanity.com/paper/2211.13234/) (2022)
- [Enhancing the Inductive Biases of Graph Neural ODE for Modeling Dynamical Systems](https://mlsanity.com/paper/2209.10740/) (2022)
- [More Than Routing: Joint GPS and Route Modeling for Refine Trajectory Representation Learning](https://mlsanity.com/paper/2402.16915/) (2024)
- [Road Network Representation Learning: A Dual Graph based Approach](https://mlsanity.com/paper/2304.07298/) (2023)
- [Micro-Macro Spatial-Temporal Graph-based Encoder-Decoder for Map-Constrained Trajectory Recovery](https://mlsanity.com/paper/2404.19141/) (2024)
- [Identifying Hidden Visits from Sparse Call Detail Record Data](https://mlsanity.com/paper/2106.12885/) (2021)

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

- [PENGUIN: Enhancing Transformer with Periodic-Nested Group Attention for Long-term Time Series Forecasting](https://mlsanity.com/paper/2508.13773/) (2025)

## Abstract (arXiv)

In real-world applications, GPS trajectories often suffer from low sampling rates, with large and irregular intervals between consecutive GPS points. This sparse characteristic presents challenges for their direct use in GPS-based systems. This paper addresses the task of map-constrained trajectory recovery, aiming to enhance trajectory sampling rates of GPS trajectories. Previous studies commonly adopt a sequence-to-sequence framework, where an encoder captures the trajectory patterns and a decoder reconstructs the target trajectory. Within this framework, effectively representing the road network and extracting relevant trajectory features are crucial for overall performance. Despite advancements in these models, they fail to fully leverage the complex spatio-temporal dynamics present in both the trajectory and the road network. To overcome these limitations, we categorize the spatio-temporal dynamics of trajectory data into two distinct aspects: spatial-temporal traffic dynamics and trajectory dynamics. Furthermore, We propose TedTrajRec, a novel method for trajectory recovery. To capture spatio-temporal traffic dynamics, we introduce PD-GNN, which models periodic patterns and learns topologically aware dynamics concurrently for each road segment. For spatio-temporal trajectory dynamics, we present TedFormer, a time-aware Transformer that incorporates temporal dynamics for each GPS location by integrating closed-form neural ordinary differential equations into the attention mechanism. This allows TedFormer to effectively handle irregularly sampled data. Extensive experiments on three real-world datasets demonstrate the superior performance of TedTrajRec. The code is publicly available at https://github.com/ysygMhdxw/TEDTrajRec/.