Artificial Neural Networks for the Estimation of Pedestrian Interaction Forces

Göttlich, Simone; Knapp, Stephan

doi:10.1007/978-3-030-50450-2_2

Cited by 9 publications

(12 citation statements)

References 26 publications

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“…First, we discuss the numerical results obtained for the social force model. We begin with plots similar to [11], where we show the results for the interaction forces by four contour plots for the x-direction and for the y-direction. For each of the plots, we fix a vector v = (v 1 , v 2 ) which describes the difference of the velocity vectors of two interaction pedestrians.…”

Section: Results For Social Force Modelmentioning

confidence: 99%

“…Similar parameter identification studies for pedestrian models have been recently introduced in [7,10] using a Bayesian probabilistic method and in [11,25] using neural networks. In contrast to [11,25], where the pedestrian speed or unknown interaction forces have been estimated, we address a more general setting that also allows for theoretical investigations and a rigorous numerical treatment. More precisely, for the neural networks we make some basic assumptions, but it is important to note that we do not prescribe any physical interaction assumptions.…”

Section: Introductionmentioning

confidence: 94%

“…To prevent this issue when training the neural networks, we use a mini-batch gradient descent scheme. Indeed, we compute ADADELTA updates as proposed in [11]. This leads to the following algorithm:…”

Section: Stochastic Descentmentioning

confidence: 99%

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Parameter calibration with stochastic gradient descent for interacting particle systems driven by neural networks

Göttlich

Totzeck

2021

Math. Control Signals Syst.

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We propose a neural network approach to model general interaction dynamics and an adjoint-based stochastic gradient descent algorithm to calibrate its parameters. The parameter calibration problem is considered as optimal control problem that is investigated from a theoretical and numerical point of view. We prove the existence of optimal controls, derive the corresponding first-order optimality system and formulate a stochastic gradient descent algorithm to identify parameters for given data sets. To validate the approach, we use real data sets from traffic and crowd dynamics to fit the parameters. The results are compared to forces corresponding to well-known interaction models such as the Lighthill–Whitham–Richards model for traffic and the social force model for crowd motion.

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Section: Results For Social Force Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 94%

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Parameter calibration with stochastic gradient descent for interacting particle systems driven by neural networks

Göttlich

Totzeck

2021

Math. Control Signals Syst.

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“…Remark 2. We emphasize that in contrast to [10] the cost functional is not of the usual structure given by 1 m…”

Section: J(x(u); Z)mentioning

confidence: 99%

“…Similar parameter identification studies for pedestrian models haven been recently introduced in [6,9] using a Bayesian probabilistic method and in [10,23] using neural networks. In contrast to [10,23], where the pedestrian speed or unknown interaction forces have been estimated, we address a more general setting that also allows for theoretical investigations and a rigorous numerical treatment. More precisely, for the neural networks we make some basic assumptions, but it is important to note that we do not prescribe any physical interaction assumptions.…”

Section: Introductionmentioning

confidence: 95%

Optimal control for interacting particle systems driven by neural networks

Göttlich,

Totzeck

2021

Preprint

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We propose a neural network approach to model general interaction dynamics and an adjoint based stochastic gradient descent algorithm to calibrate its parameters. The parameter calibration problem is considered as optimal control problem that is investigated from a theoretical and numerical point of view. We prove the existence of optimal controls, derive the corresponding first order optimality system and formulate a stochastic gradient descent algorithm to identify parameters for given data sets. To validate the approach we use real data sets from traffic and crowd dynamics to fit the parameters. The results are compared to forces corresponding to well-known interaction models such as the Lighthill-Whitham-Richards model for traffic and the social force model for crowd motion.

show abstract