Related papers: Overview on uncertainty quantification in traffic …

We consider the application of deep generative models in propagating uncertainty through complex physical systems. Specifically, we put forth an implicit variational inference formulation that constrains the generative model output to…

We present a new statistically driven method for analyzing the modeling of geophysical flows. Many models have been advocated by different modelers for such flows incorporating different modeling assumptions. Limited and sparse…

The stochastic variational approach for geophysical fluid dynamics was introduced by Holm (Proc Roy Soc A, 2015) as a framework for deriving stochastic parameterisations for unresolved scales. This paper applies the variational stochastic…

In this paper, we present a new approach that generalizes the existing second-order hydrodynamic traffic models. In the proposed approach, we use the expression for the relative velocity of disturbances propagation in traffic flow. We show…

We study an identification problem which estimates the parameters of the underlying random distribution for uncertain scalar conservation laws. The hyperbolic equations are discretized with the so-called discontinuous stochastic Galerkin…

Autonomous vehicles are expected to navigate in complex traffic scenarios with multiple surrounding vehicles. The correlations between road users vary over time, the degree of which, in theory, could be infinitely large, thus posing a great…

Statistical properties of circulation encode relevant information about the multi-scale structure of turbulent cascades. Recent massive computational efforts have posed challenging theoretical issues, as the dependence of circulation…

The goal of this research is to derive an approach to assess uncertainty in an arbitrary volume conditioned by sampling data, without using geostatistical simulation. We have accomplished this goal by deriving an numerical tool suitable for…

This article aims at discovering the unknown variables in the system through data analysis. The main idea is to use the time of data collection as a surrogate variable and try to identify the unknown variables by modeling gradual and sudden…

This is a set of four lectures devoted to simple ideas about turbulent transport, a ubiquitous non-equilibrium phenomenon. In the course similar to that given by the author in 2006 in Warwick [45], we discuss lessons which have been learned…

Logistic regression is an important statistical tool for assessing the probability of an outcome based upon some predictive variables. Standard methods can only deal with precisely known data, however many datasets have uncertainties which…

We address the problem of uncertainty quantification for graph-structured data, or, more specifically, the problem to quantify the predictive uncertainty in (semi-supervised) node classification. Key questions in this regard concern the…

Traffic safety at intersections is studied quantitatively using methods from Statistical Mechanics on the basis of simple microscopic traffic flow models. In order to determine a relationship between traffic flow and the number of crashes,…

A simple model to handle the flow of people in emergency evacuation situations is considered: at every point x, the velocity U(x) that individuals at x would like to realize is given. Yet, the incompressibility constraint prevents this…

We introduce a class of stochastic advection problems amenable to analysis of turbulent transport. The statistics of the flow field are represented as a continuous time Markov process, a choice that captures the intuitive notion of…

In autonomous driving, accurate motion prediction is crucial for safe and efficient motion planning. To ensure safety, planners require reliable uncertainty estimates of the predicted behavior of surrounding agents, yet this aspect has…

Graph Neural Networks (GNN) provide a powerful framework that elegantly integrates Graph theory with Machine learning for modeling and analysis of networked data. We consider the problem of quantifying the uncertainty in predictions of GNN…

We develop a general theory dealing with stochastic models for dynamical systems that are governed by various nonlinear, ordinary or partial differential, equations. In particular, we address the problem how flows in the random medium…

We propose a macroscopic traffic network flow model suitable for analysis as a dynamical system, and we qualitatively analyze equilibrium flows as well as convergence. Flows at a junction are determined by downstream supply of capacity as…

We propose a model describing the traffic flow on a road with variable widths in this paper. The model, which is modified the Aw-Rascle model, is not conservative because of the source term. We obtain the elementary waves of the new traffic…