# Evaluation of Differentially Constrained Motion Models for Graph-Based Trajectory Prediction

arXiv: https://arxiv.org/abs/2304.05116 · HTML: https://mlsanity.com/paper/2304.05116/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 39 references that are in the map.
- First posted on arXiv 11 Apr 2023.

## Builds on (most cited first, 22 of 22)

- [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)
- [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)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [On the Properties of Neural Machine Translation: Encoder-Decoder Approaches](https://mlsanity.com/paper/1409.1259/) (2014)
- [How Attentive are Graph Attention Networks?](https://mlsanity.com/paper/2105.14491/) (2021)
- [Cyclical Learning Rates for Training Neural Networks](https://mlsanity.com/paper/1506.01186/) (2015)
- [The highD Dataset: A Drone Dataset of Naturalistic Vehicle Trajectories on German Highways for Validation of Highly Automated Driving Systems](https://mlsanity.com/paper/1810.05642/) (2018)
- [A Survey of Motion Planning and Control Techniques for Self-driving Urban Vehicles](https://mlsanity.com/paper/1604.07446/) (2016)
- [Convolutional Social Pooling for Vehicle Trajectory Prediction](https://mlsanity.com/paper/1805.06771/) (2018)
- [Multimodal Motion Prediction with Stacked Transformers](https://mlsanity.com/paper/2103.11624/) (2021)
- [Multi-modal Motion Prediction with Transformer-based Neural Network for Autonomous Driving](https://mlsanity.com/paper/2109.06446/) (2021)
- [Spatio-Temporal Graph Dual-Attention Network for Multi-Agent Prediction and Tracking](https://mlsanity.com/paper/2102.09117/) (2021)
- [Probabilistic Prediction of Vehicle Semantic Intention and Motion](https://mlsanity.com/paper/1804.03629/) (2018)
- [Deep Learning-based Vehicle Behaviour Prediction For Autonomous Driving Applications: A Review](https://mlsanity.com/paper/1912.11676/) (2019)
- [MTP-GO: Graph-Based Probabilistic Multi-Agent Trajectory Prediction with Neural ODEs](https://mlsanity.com/paper/2302.00735/) (2023)
- [SCALE-Net: Scalable Vehicle Trajectory Prediction Network under Random Number of Interacting Vehicles via Edge-enhanced Graph Convolutional Neural Network](https://mlsanity.com/paper/2002.12609/) (2020)
- [Scenario-Transferable Semantic Graph Reasoning for Interaction-Aware Probabilistic Prediction](https://mlsanity.com/paper/2004.03053/) (2020)
- [Online Joint State Inference and Learning of Partially Unknown State-Space Models](https://mlsanity.com/paper/2102.07418/) (2021)
- [Vehicle Behavior Prediction and Generalization Using Imbalanced Learning Techniques](https://mlsanity.com/paper/2109.10656/) (2021)
- [Temporal Graph Neural Networks for Irregular Data](https://mlsanity.com/paper/2302.08415/) (2023)

## Built on by (most cited first, 6 of 6)

- [Diffusion-Based Environment-Aware Trajectory Prediction](https://mlsanity.com/paper/2403.11643/) (2024)
- [Trajectory Prediction for Autonomous Driving: Progress, Limitations, and Future Directions](https://mlsanity.com/paper/2503.03262/) (2025)
- [Graph ODEs and Beyond: A Comprehensive Survey on Integrating Differential Equations with Graph Neural Networks](https://mlsanity.com/paper/2503.23167/) (2025)
- [MAP-Former: Multi-Agent-Pair Gaussian Joint Prediction](https://mlsanity.com/paper/2404.19283/) (2024)
- [Toward Unified Practices in Trajectory Prediction Research on Bird's-Eye-View Datasets](https://mlsanity.com/paper/2405.00604/) (2024)
- [Unveiling Transferability in Trajectory Prediction via Latent Scene Embeddings](https://mlsanity.com/paper/2606.30777/) (2026)

## Abstract (arXiv)

Given their flexibility and encouraging performance, deep-learning models are becoming standard for motion prediction in autonomous driving. However, with great flexibility comes a lack of interpretability and possible violations of physical constraints. Accompanying these data-driven methods with differentially-constrained motion models to provide physically feasible trajectories is a promising future direction. The foundation for this work is a previously introduced graph-neural-network-based model, MTP-GO. The neural network learns to compute the inputs to an underlying motion model to provide physically feasible trajectories. This research investigates the performance of various motion models in combination with numerical solvers for the prediction task. The study shows that simpler models, such as low-order integrator models, are preferred over more complex, e.g., kinematic models, to achieve accurate predictions. Further, the numerical solver can have a substantial impact on performance, advising against commonly used first-order methods like Euler forward. Instead, a second-order method like Heun's can greatly improve predictions.