# Trajectory Prediction using Equivariant Continuous Convolution

arXiv: https://arxiv.org/abs/2010.11344 · HTML: https://mlsanity.com/paper/2010.11344/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Oct 2020.

## Built on by (most cited first, 26 of 26)

- [Approximately Equivariant Networks for Imperfectly Symmetric Dynamics](https://mlsanity.com/paper/2201.11969/) (2022)
- [Learning Symmetric Embeddings for Equivariant World Models](https://mlsanity.com/paper/2204.11371/) (2022)
- [Physics-Guided Deep Learning for Dynamical Systems: A Survey](https://mlsanity.com/paper/2107.01272/) (2021)
- [EDGI: Equivariant Diffusion for Planning with Embodied Agents](https://mlsanity.com/paper/2303.12410/) (2023)
- [The Surprising Effectiveness of Equivariant Models in Domains with Latent Symmetry](https://mlsanity.com/paper/2211.09231/) (2022)
- [Guaranteed Conservation of Momentum for Learning Particle-based Fluid Dynamics](https://mlsanity.com/paper/2210.06036/) (2022)
- [Roto-translated Local Coordinate Frames For Interacting Dynamical Systems](https://mlsanity.com/paper/2110.14961/) (2021)
- [Discovering Symmetry Breaking in Physical Systems with Relaxed Group Convolution](https://mlsanity.com/paper/2310.02299/) (2023)
- [A General Theory of Correct, Incorrect, and Extrinsic Equivariance](https://mlsanity.com/paper/2303.04745/) (2023)
- [Lorentz group equivariant autoencoders](https://mlsanity.com/paper/2212.07347/) (2022)
- [Neurosymbolic Grounding for Compositional World Models](https://mlsanity.com/paper/2310.12690/) (2023)
- [On Robot Grasp Learning Using Equivariant Models](https://mlsanity.com/paper/2306.06489/) (2023)
- [MFTraj: Map-Free, Behavior-Driven Trajectory Prediction for Autonomous Driving](https://mlsanity.com/paper/2405.01266/) (2024)
- [Improving the Sample-Complexity of Deep Classification Networks with Invariant Integration](https://mlsanity.com/paper/2202.03967/) (2022)
- [Latent Field Discovery In Interacting Dynamical Systems With Neural Fields](https://mlsanity.com/paper/2310.20679/) (2023)
- [3D Equivariant Visuomotor Policy Learning via Spherical Projection](https://mlsanity.com/paper/2505.16969/) (2025)
- [Pioneering SE(2)-Equivariant Trajectory Planning for Automated Driving](https://mlsanity.com/paper/2403.11304/) (2024)
- [Distance-Based Tree-Sliced Wasserstein Distance](https://mlsanity.com/paper/2503.11050/) (2025)
- [Physics-enhanced Neural Networks in the Small Data Regime](https://mlsanity.com/paper/2111.10329/) (2021)
- [Efficient Baselines for Motion Prediction in Autonomous Driving](https://mlsanity.com/paper/2309.03387/) (2023)
- [Equivariant Deep Dynamical Model for Motion Prediction](https://mlsanity.com/paper/2111.01892/) (2021)
- [Probabilistic Symmetry for Multi-Agent Dynamics](https://mlsanity.com/paper/2205.01927/) (2022)
- [Spherical Tree-Sliced Wasserstein Distance](https://mlsanity.com/paper/2503.11249/) (2025)
- [Symmetry-aware Neural Architecture for Embodied Visual Navigation](https://mlsanity.com/paper/2112.09515/) (2021)
- [Exploring Map-based Features for Efficient Attention-based Vehicle Motion Prediction](https://mlsanity.com/paper/2205.13071/) (2022)
- [Quasi-Equivariant Metanetworks](https://mlsanity.com/paper/2604.23720/) (2026)

## Abstract (arXiv)

Trajectory prediction is a critical part of many AI applications, for example, the safe operation of autonomous vehicles. However, current methods are prone to making inconsistent and physically unrealistic predictions. We leverage insights from fluid dynamics to overcome this limitation by considering internal symmetry in real-world trajectories. We propose a novel model, Equivariant Continous COnvolution (ECCO) for improved trajectory prediction. ECCO uses rotationally-equivariant continuous convolutions to embed the symmetries of the system. On both vehicle and pedestrian trajectory datasets, ECCO attains competitive accuracy with significantly fewer parameters. It is also more sample efficient, generalizing automatically from few data points in any orientation. Lastly, ECCO improves generalization with equivariance, resulting in more physically consistent predictions. Our method provides a fresh perspective towards increasing trust and transparency in deep learning models.