# Learning Heterogeneous Interaction Strengths by Trajectory Prediction with Graph Neural Network

arXiv: https://arxiv.org/abs/2208.13179 · HTML: https://mlsanity.com/paper/2208.13179/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 35 references that are in the map.
- First posted on arXiv 28 Aug 2022.

## Builds on (most cited first, 18 of 18)

- [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)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Linformer: Self-Attention with Linear Complexity](https://mlsanity.com/paper/2006.04768/) (2020)
- [How Attentive are Graph Attention Networks?](https://mlsanity.com/paper/2105.14491/) (2021)
- [Efficient Attention: Attention with Linear Complexities](https://mlsanity.com/paper/1812.01243/) (2018)
- [Neural Relational Inference for Interacting Systems](https://mlsanity.com/paper/1802.04687/) (2018)
- [GroupNet: Multiscale Hypergraph Neural Networks for Trajectory Prediction with Relational Reasoning](https://mlsanity.com/paper/2204.08770/) (2022)
- [Multilayer Networks](https://mlsanity.com/paper/1309.7233/) (2013)
- [VAIN: Attentional Multi-agent Predictive Modeling](https://mlsanity.com/paper/1706.06122/) (2017)
- [Adaptive Trajectory Prediction via Transferable GNN](https://mlsanity.com/paper/2203.05046/) (2022)
- [A Memory-Network Based Solution for Multivariate Time-Series Forecasting](https://mlsanity.com/paper/1809.02105/) (2018)
- [A General Deep Learning Framework for Network Reconstruction and Dynamics Learning](https://mlsanity.com/paper/1812.11482/) (2018)
- [Factorised Neural Relational Inference for Multi-Interaction Systems](https://mlsanity.com/paper/1905.08721/) (2019)
- [Interaction Modeling with Multiplex Attention](https://mlsanity.com/paper/2208.10660/) (2022)
- [Learning interaction rules from multi-animal trajectories via augmented behavioral models](https://mlsanity.com/paper/2107.05326/) (2021)
- [Learning Dynamics and Structure of Complex Systems Using Graph Neural Networks](https://mlsanity.com/paper/2202.10996/) (2022)

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

- [Interpretable Machine Learning in Physics: A Review](https://mlsanity.com/paper/2503.23616/) (2025)
- [MBDS: A Multi-Body Dynamics Simulation Dataset for Graph Networks Simulators](https://mlsanity.com/paper/2410.03107/) (2024)
- [ART: Adaptive Relational Transformer for Pedestrian Trajectory Prediction with Temporal-Aware Relations](https://mlsanity.com/paper/2604.03649/) (2026)
- [Interpretable Relational Inference with LLM-Guided Symbolic Dynamics Modeling](https://mlsanity.com/paper/2604.12806/) (2026)

## Abstract (arXiv)

Dynamical systems with interacting agents are universal in nature, commonly modeled by a graph of relationships between their constituents. Recently, various works have been presented to tackle the problem of inferring those relationships from the system trajectories via deep neural networks, but most of the studies assume binary or discrete types of interactions for simplicity. In the real world, the interaction kernels often involve continuous interaction strengths, which cannot be accurately approximated by discrete relations. In this work, we propose the relational attentive inference network (RAIN) to infer continuously weighted interaction graphs without any ground-truth interaction strengths. Our model employs a novel pairwise attention (PA) mechanism to refine the trajectory representations and a graph transformer to extract heterogeneous interaction weights for each pair of agents. We show that our RAIN model with the PA mechanism accurately infers continuous interaction strengths for simulated physical systems in an unsupervised manner. Further, RAIN with PA successfully predicts trajectories from motion capture data with an interpretable interaction graph, demonstrating the virtue of modeling unknown dynamics with continuous weights.