# Deep Social Force

arXiv: https://arxiv.org/abs/2109.12081 · HTML: https://mlsanity.com/paper/2109.12081/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 45 references that are in the map.
- First posted on arXiv 24 Sep 2021.

## Builds on (most cited first, 5 of 5)

- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Social GAN: Socially Acceptable Trajectories with Generative Adversarial Networks](https://mlsanity.com/paper/1803.10892/) (2018)
- [Crowd-Robot Interaction: Crowd-aware Robot Navigation with Attention-based Deep Reinforcement Learning](https://mlsanity.com/paper/1809.08835/) (2018)
- [Human Trajectory Forecasting in Crowds: A Deep Learning Perspective](https://mlsanity.com/paper/2007.03639/) (2020)
- [A Data-driven Model for Interaction-aware Pedestrian Motion Prediction in Object Cluttered Environments](https://mlsanity.com/paper/1709.08528/) (2017)

## Built on by (most cited first, 8 of 8)

- [Human Trajectory Prediction via Neural Social Physics](https://mlsanity.com/paper/2207.10435/) (2022)
- [Review of Pedestrian Trajectory Prediction Methods: Comparing Deep Learning and Knowledge-based Approaches](https://mlsanity.com/paper/2111.06740/) (2021)
- [Human Trajectory Forecasting with Explainable Behavioral Uncertainty](https://mlsanity.com/paper/2307.01817/) (2023)
- [Learning Implicit Social Navigation Behavior using Deep Inverse Reinforcement Learning](https://mlsanity.com/paper/2501.06946/) (2025)
- [SFMGNet: A Physics-based Neural Network To Predict Pedestrian Trajectories](https://mlsanity.com/paper/2202.02791/) (2022)
- [Pedestrian-Aware Motion Planning for Autonomous Driving in Complex Urban Scenarios](https://mlsanity.com/paper/2504.01409/) (2025)
- [Improving Generalization in Reinforcement Learning Training Regimes for Social Robot Navigation](https://mlsanity.com/paper/2308.14947/) (2023)
- [Automatic Gradient Estimation for Calibrating Crowd Models with Discrete Decision Making](https://mlsanity.com/paper/2404.04678/) (2024)

## Abstract (arXiv)

The Social Force model introduced by Helbing and Molnar in 1995 is a cornerstone of pedestrian simulation. This paper introduces a differentiable simulation of the Social Force model where the assumptions on the shapes of interaction potentials are relaxed with the use of universal function approximators in the form of neural networks. Classical force-based pedestrian simulations suffer from unnatural locking behavior on head-on collision paths. In addition, they cannot model the bias of pedestrians to avoid each other on the right or left depending on the geographic region. My experiments with more general interaction potentials show that potentials with a sharp tip in the front avoid locking. In addition, asymmetric interaction potentials lead to a left or right bias when pedestrians avoid each other.