In this session we concentrate on the latest research insights for uncertainty quantification in transport problems and high-dimensional systems under structural uncertainties, with focus on kinetic and hyperbolic PDEs and multiscale interacting particle systems.
14:00
Multi-agent systems with uncertain interactions: the case of vehicular traffic
Andrea Tosin | Politecnico di Torino | Italy
Show details
Author:
Andrea Tosin | Politecnico di Torino | Italy
In this talk, we will discuss a mathematical framework, based on the Boltzmann-type kinetic theory, to study multi-agent systems with structurally uncertain microscopic interactions. In particular, we will focus on the case in which the interactions include uncertain parameters, which represent a typically unavoidable imperfect knowledge of the fundamental dynamics of the system under consideration. Then, by referring specifically to the case of vehicular traffic, we will discuss the impact of the microscopic uncertainties on the predictable aggregate trends. Finally, if the time allows, we will give some hints about possible bottom-up control strategies aimed at damping the propagation of such uncertainties across the scales.
14:30
Intrusive acceleration techniques for uncertainty quantification
Jonas Kusch | Karlsruher Institut für Technologie | Germany
Show details
Author:
Jonas Kusch | Karlsruher Institut für Technologie | Germany
In this talk, we propose acceleration techniques for the IPM method, putting the main focus on steady problems. When using pseudo-time steps to iterate the moments to a steady state, we propose to not fully converge the optimization problem in every step. In fact, we perform only a single Newton iteration towards the exact minimizer, i.e. we simultaneously iterates both, the dual variables of the optimization problem as well as the moments to a steady state. Consequently, the numerical costs of performing the entropy reconstruction are significantly decreased. Additionally, we make use of the intrusive nature of IPM by locally refining the stochastic space in regions with non-smooth solutions. We demonstrate the effectiveness of the proposed strategies by presenting results from fluid dynamics and particle transport which we compare against results obtained with non-intrusive methods.
15:00
Reconstructing phonon transmission coefficients at solid interfaces using metrology
Anjali Nair | University of Wisconsin-Madison | United States
Show details
Author:
Anjali Nair | University of Wisconsin-Madison | United States
Interfaces play an essential role in phonon-mediated heat conduction in solids. Material discontinuities lead to thermal phonon reflections and it plays an increasingly important role in applications, particularly as device sizes decrease below the intrinsic mean free paths (MFPs) of thermal phonons. In this work, we study the unique reconstruction of reflection coefficient in the phonon transport equation using the measurement of the temperature at the surface of the material. The temperature has continuous dependence on the reflection coefficient, and thus the uncertainties in the measurement are continuously mapped to the uncertainties in the reflection coefficients. We also formulate a minimization problem for the numerical reconstruction and will present an associated stochastic gradient descent method.