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Deep Social Force

Sven Kreiss

arXiv:2109.12081v1cs.LG

TL;DR

Force-based pedestrian simulations struggle with head-on avoidance and do not capture regional side biases. This paper generalizes Social Force potentials with neural networks while retaining the model's interpretable structure; experiments recover a synthetic potential and show that asymmetric potentials produce a left-right avoidance bias.

  • Problem

    Force-based pedestrian simulations show unnatural behavior during head-on avoidance, and do not model right-side avoidance in continental western Europe.

    Source: §1 · p. 1

  • Method

    The method replaces fixed potential shapes with neural networks while retaining Social Force structure and interpretable forces derived from potential gradients.

    Source: §1 · pp. 1–2

  • Results

    The differentiable simulation recovers the generating potential on synthetic data, while asymmetric potentials produce a left-right bias in corridor avoidance.

    Source: §5 · pp. 8–9

  • Takeaways & Limitations

    Learned interaction potentials retain interpretable shapes that can be plotted, while allowing asymmetric forms that model pedestrians preferring the right side of a corridor.

    Source: §5 · p. 9, §6 · p. 10

    Most experiments use toy problems, and the authors note that coordinate-based path forecasting may be less valid in open spaces where motion is driven by factors outside trajectory coordinates.

    Source: §6 · pp. 10–11

Abstract

from arXiv · show

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.

1. Introduction

The paper targets unnatural head-on avoidance and limited regional side-bias modeling by generalizing Social Force interaction potentials without sacrificing interpretability. It replaces fixed potential shapes with neural networks while retaining forces derived from potential gradients.

1. Introduction

  • Force-based pedestrian models show unnatural head-on avoidance, and simulations do not capture right-side avoidance in continental western Europe.The paper identifies this as limiting applications to corridor counterflows.Source: §1 · p. 1
  • Deep learning generalizes Social Force interaction potentials while preserving interpretable forces derived from scalar-potential gradients.The method avoids a black-box replacement of the entire model.Source: §1 · pp. 1–2
  • Fixed parametric shapes, such as falling exponentials, constrain interaction potentials; arbitrary continuous differentiable functions could retain interpretability without that constraint.Source: §1 · p. 1
  • Deep neural networks act as universal function approximators for interaction potentials, with Social Forces obtained from their gradients using automatic differentiation.The same automatic differentiation implementation computes potential gradients.Source: §1 · pp. 1–2
  • The potentials are inferred from observed pedestrian paths, allowing an optimizer to adjust their shapes so predicted paths match true paths.Figure 1 illustrates the force as the gradient of a repulsive potential surrounding another pedestrian.Source: §1 · p. 2, Figure 1 · p. 2

2. Related Work

Prior work spans interpretable hand-crafted force models and higher-capacity data-driven interaction models. The paper positions Deep Social Force as a non-parametric approach intended to combine model interpretability with the capacity to represent complex interactions.

2. Related Work

  • Interpretable models use hand-crafted energy potentials, while high-capacity data-driven models can learn more generic interactions but are difficult to interpret.The Social Force model has been used in pedestrian modeling, crowd behavior, robotics, and activity understanding.Source: §2 · p. 3
  • Manually chosen potential functions limit the predictive power of interpretable models, despite their role in making model behavior analyzable.Source: §2 · p. 3
  • Data-driven recurrent neural network methods represent interactions through social tensors or adversarial trajectory-distribution training, but their interaction mechanisms are difficult to understand.The passage also notes these methods are data hungry compared with hand-crafted methods.Source: §2 · p. 3
  • Deep Social Force is proposed to combine the benefits of interpretable and high-capacity approaches through a non-parametric model.Source: §2 · p. 3

3. Social Force Examples

The paper reproduces selected toy examples from the original Social Force work and reports a gate-grouping behavior that depends on pedestrians having different preferred speeds.

3. Social Force Examples

  • The paper re-implements several toy examples from the original Social Force paper using modern software tools and open-sources them.Source: §3 · p. 4
  • The corridor example reproduces opposing pedestrian flows, with filled and empty circles indicating opposite goals and circle size indicating walking speed.The original lane-forming study is not reproduced; a later extension examines left-right asymmetries.Source: §3 · p. 4
  • The reproduced gate example shows groups of a few pedestrians passing at a time, and this behavior appears only with a preferred walking-speed distribution.Source: §3 · p. 4
  • The baseline implementation vectorizes operations and integrates motion with LeapFrog at 25 steps per second.Source: §3 · p. 4

4. Method

Deep Social Force aims to make the Social Force model more expressive while retaining its interpretable force structure. It replaces parametric potentials with neural networks and uses automatic differentiation to obtain forces and parameter gradients.

4. Method

  • Figure 3 illustrates opposing pedestrian flows at a gate, with circle size encoding walking speed.Five pedestrians have reached the left goal, four the right, and a group of two is passing rightward.Source: Figure 3 · p. 5
  • The conventional human-human interaction potential is a falling exponential in b; a multi-layer perceptron replaces that parametric form.The conventional potential’s optimizable parameters are its peak value and width, while the neural replacement uses linear operators and Softplus.Source: §4 · p. 6
  • Neural networks replace hand-engineered potential shapes, allowing the model to discover potential properties from data while retaining interpretable forces.The stated longer-term aim is to calibrate models on larger pedestrian datasets.Source: §4 · pp. 4–6
  • Automatic differentiation computes potential gradients for forces and parameter gradients for SGD from simulations of observed pedestrian paths.The potentials are inferred indirectly because they are not directly observed.Source: §4 · pp. 5–6
  • For multidimensional potentials, the MLP takes b and parallel and perpendicular distances after transforming each input into 64 Fourier features.The three input transformations yield 192 Fourier features in total.Source: §4 · p. 6

5. Results

Experiments show that differentiable Social Force simulations can recover interaction potentials from synthetic paths and infer asymmetric potentials that produce right-side corridor passing. A first real-world fitting attempt did not converge and depended on synthetic-data initialization.

Automatic Differentiation of Potentials

  • Back-propagated gradients make finite differences more than an order of magnitude slower even for a 10-parameter MLP, and support inference with over 10,000 parameters.Finite-difference methods are described as infeasible for larger MLPs.Source: §5 · pp. 7–8

Baseline: Parameter Inference for 1D MLP

  • The differentiable simulation with SGD recovers the exact generating potential from a synthetic path, although the inferred MLP is not constrained to the generator’s falling-exponential form.Figure 5 shows the fit to a single synthetic path.Source: §5 · p. 8, Figure 5 · p. 8

Asymmetric 2D Potentials

  • On synthetic data generated with an asymmetric potential, the approximately 10,000-parameter 2D MLP infers an asymmetric potential.The inferred potential is visualized in Figure 6b.Source: Figure 6 · p. 8, §5 · p. 9
  • After 40s, pedestrians initialized randomly all move to the right in their walking direction to avoid others in the asymmetric-potential corridor simulation.The figure explains that pedestrians prefer the right side of oncoming pedestrians.Source: §5 · p. 9, Figure 7 · p. 9

Inference from real data

  • On the real-world Crowd by Example scene, optimization does not converge and fitting does not work without synthetic-data initialization.The tentative inferred potential is repulsive below b = 1 m and attractive above b = 1 m; the author suggests social groups may explain the attractive regime.Source: §5 · pp. 9–10, Figure 8 · p. 10

6. Conclusion

The paper and its open-source software offer an entry point to reproducible research and critical examination of previous claims. The authors note that the work focuses mostly on toy problems and that its forecasting assumption may fit crowded corridors better than open campus spaces.

6. Conclusion

  • The paper and its open-source software provide an entry point to reproducible research and allow critical investigation of previous claims.Source: §6 · p. 10
  • Most of the paper focuses on toy problems, and the authors say real-data applications generally disappoint; they leave open whether the model or forecasting premise is inadequate.They question whether forecasting paths from a few seconds of observed coordinates is too optimistic in general situations.Source: §6 · p. 10
  • Forecasting from short trajectory observations may fit crowded train-station corridors better than open campus spaces, where motion is driven by factors absent from trajectory coordinates.Source: §6 · pp. 10–11
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