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pro vyhledávání: '"VISCONTI, G."'
Residual deep neural networks (ResNets) are mathematically described as interacting particle systems. In the case of infinitely many layers the ResNet leads to a system of coupled system of ordinary differential equations known as neural differential
Externí odkaz:
http://arxiv.org/abs/2112.14150
We study a hierarchy of models based on kinetic equations for the descriptions of traffic flow in presence of autonomous and human--driven vehicles. The autonomous cars considered in this paper are thought of as vehicles endowed with some degree of a
Externí odkaz:
http://arxiv.org/abs/2107.14081
Many interesting applications of hyperbolic systems of equations are stiff, and require the time step to satisfy restrictive stability conditions. One way to avoid small time steps is to use implicit time integration. Implicit integration is quite st
Externí odkaz:
http://arxiv.org/abs/2102.00741
This paper extends the ensemble Kalman filter (EnKF) for inverse problems to identify trending model coefficients. This is done by repeatedly inflating the ensemble while maintaining the mean of the particles. As a benchmark serves a classic EnKF and
Externí odkaz:
http://arxiv.org/abs/2001.10861
We study kinetic models for traffic flow characterized by the property of producing backward propagating waves. These waves may be identified with the phenomenon of stop-and-go waves typically observed on highways. In particular, a refined modeling o
Externí odkaz:
http://arxiv.org/abs/2002.02802
Nowadays, neural networks are widely used in many applications as artificial intelligence models for learning tasks. Since typically neural networks process a very large amount of data, it is convenient to formulate them within the mean-field and kin
Externí odkaz:
http://arxiv.org/abs/2001.04294
Publikováno v:
In G. Puppo, A. Tosin, Eds., Mathematical Descriptions of Traffic Flow: Micro, Macro and Kinetic Models SEMA SIMAI Springer Series, volume 12, pages 1-16. Springer, 2021
In this work we investigate the ability of a kinetic approach for traffic dynamics to predict speed distributions obtained through rough data. The present approach adopts the formalism of uncertainty quantification, since reaction strengths are uncer
Externí odkaz:
http://arxiv.org/abs/1912.03706
In this paper, properties of a recently proposed mathematical model for data flow in large-scale asynchronous computer systems are analyzed. In particular, the existence of special weak solutions based on propagating fronts is established. Qualitativ
Externí odkaz:
http://arxiv.org/abs/1910.10117
Akademický článek
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Publikováno v:
MATHEMATICS OF COMPUTATION Volume 87, Number 312, July 2018, Pages 1689-1719
In this paper we introduce a general framework for defining and studying essentially non-oscillatory reconstruction procedures of arbitrarily high order accuracy, interpolating data in a central stencil around a given computational cell ($\CWENO$). T
Externí odkaz:
http://arxiv.org/abs/1607.07319