Model-based assessment of the impact of driver-assist vehicles using kinetic theory

Piccoli, Benedetto; Tosin, Andrea; Zanella, Mattia

doi:10.1007/s00033-020-01383-9

Cited by 31 publications

(33 citation statements)

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“…Automated traffic flow dynamics have been modelled recently as cruise controls implemented either in the vehicle-to-vehicle interactions, see e.g. [15,29,35,44], or directly in the aggregate traffic dynamics [11,12]. In general, the effect of such controls is the stabilisation of the traffic flow depending on the penetration rate of the automated vehicles, as also testified by the field experiment reported in [40].…”

Section: +λmentioning

confidence: 99%

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Uncertainty damping in kinetic traffic models by driver-assist controls

Tosin¹,

Zanella²

2021

MCRF

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In this paper, we propose a kinetic model of traffic flow with uncertain binary interactions, which explains the scattering of the fundamental diagram in terms of the macroscopic variability of aggregate quantities, such as the mean speed and the flux of the vehicles, produced by the microscopic uncertainty. Moreover, we design control strategies at the level of the microscopic interactions among the vehicles, by which we prove that it is possible to dampen the propagation of such an uncertainty across the scales. Our analytical and numerical results suggest that the aggregate traffic flow may be made more ordered, hence predictable, by implementing such control protocols in driver-assist vehicles. Remarkably, they also provide a precise relationship between a measure of the macroscopic damping of the uncertainty and the penetration rate of the driver-assist technology in the traffic stream.

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Section: +λmentioning

confidence: 99%

“…whence, from (35) with U := supp ϕ ∪ supp ϕ ⊂⊂ (0, 1), Let now p, q ∈ [1, +∞] be such that 1 p + 1 q = 1. Hölder's and Chebyshev's inequalities imply…”

Section: 22mentioning

confidence: 99%

Uncertainty damping in kinetic traffic models by driver-assist controls

Tosin¹,

Zanella²

2021

MCRF

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“…Beyond theory, FPE is also a common tool to model real-world phenomena. For example, it has been used to determine the first passage time from one protein conformation to another 4 , to describe the weights of deep networks when updating them using stochastic gradient descent 5 , to characterize the behavior of driver-assist vehicles in freeway traffic 6 and to model the distribution of the personal wealth in socio-economics 7 . In all these applications on real-world pdfs, the FPE terms are proposed first and then validated by comparing the calculated pdf with the experimental data, which can be seen as a forward problem.…”

Section: Introductionmentioning

confidence: 99%

Solving the inverse problem of time independent Fokker–Planck equation with a self supervised neural network method

Liu

Kou

Park

et al. 2021

Sci Rep

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The Fokker–Planck equation (FPE) has been used in many important applications to study stochastic processes with the evolution of the probability density function (pdf). Previous studies on FPE mainly focus on solving the forward problem which is to predict the time-evolution of the pdf from the underlying FPE terms. However, in many applications the FPE terms are usually unknown and roughly estimated, and solving the forward problem becomes more challenging. In this work, we take a different approach of starting with the observed pdfs to recover the FPE terms using a self-supervised machine learning method. This approach, known as the inverse problem, has the advantage of requiring minimal assumptions on the FPE terms and allows data-driven scientific discovery of unknown FPE mechanisms. Specifically, we propose an FPE-based neural network (FPE-NN) which directly incorporates the FPE terms as neural network weights. By training the network on observed pdfs, we recover the FPE terms. Additionally, to account for noise in real-world observations, FPE-NN is able to denoise the observed pdfs by training the pdfs alongside the network weights. Our experimental results on various forms of FPE show that FPE-NN can accurately recover FPE terms and denoising the pdf plays an essential role.

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Section: Introductionmentioning

confidence: 99%

Self-supervised Learning Method to Solve the Inverse Problem of Fokker-Planck Equation

Liu

Kou

Park

et al. 2021

Preprint

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The Fokker-Planck equation (FPE) has been used in many important applications to study stochastic processes with the evolution of the probability density function (pdf). Previous studies on FPE mainly focus on solving the forward problem which is to predict the time-evolution of the pdf from the underlying FPE terms. However, in many applications the FPE terms are usually unknown and roughly estimated, and solving the forward problem becomes more challenging. In this work, we take a different approach of starting with the observed pdfs to recover the FPE terms using a self-supervised machine learning method. This approach, known as the inverse problem, has the advantage of requiring minimal assumptions on the FPE terms and allows data-driven scientific discovery of unknown FPE mechanisms. Specifically, we propose an FPE-based neural network (FPE-NN) which directly incorporates the FPE terms as neural network weights. By training the network on observed pdfs, we recover the FPE terms. Additionally, to account for noise in real-world observations, FPE-NN is able to denoise the observed pdfs by training the pdfs alongside the network weights. Our experimental results on various forms of FPE show that FPE-NN can accurately recover FPE terms and denoising the pdf plays an essential role.

show abstract

Model-based assessment of the impact of driver-assist vehicles using kinetic theory

Cited by 31 publications

References 50 publications

Uncertainty damping in kinetic traffic models by driver-assist controls

Uncertainty damping in kinetic traffic models by driver-assist controls

Solving the inverse problem of time independent Fokker–Planck equation with a self supervised neural network method

Self-supervised Learning Method to Solve the Inverse Problem of Fokker-Planck Equation

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