Many systems of interest can be described as a large number of particles that interact in a highly non-intuitive way. In pollution, for example, these particles can be fine dust or aerosol particles, in mobility they are individual vehicles, in financial systems, they are individual banks or even consumers. Mathematical models of interacting particles are often based on hyperbolic or kinetic models, which provide a common mathematical structure. Hyperbolic models give a macroscopic description, in terms of particle density, momentum and energy. Kinetic models describe the system at a more microscopic level and contain detailed information about individual particle interactions.

Current challenges force scientists to take into account the precise (microscopic) interactions between individual particles, as these interactions directly influence the behaviour that emerges at the macroscopic scale of interest. At the same time, the availability of massive amounts of measurement data allows the calibration of increasingly complex models. Nevertheless, computer simulation of interacting particle systems is usually done with highly approximate (macroscopic) models to reduce computational complexity. Facing these challenges without sacrificing the complexity of the underlying particle interactions requires a fundamentally new type of scientist that uses an interdisciplinary approach and a solid mathematical underpinning. Hence, in the DATAHYKING Doctoral Network, we aim at training a new generation of modeling and simulation experts to develop virtual experimentation tools and workflows that can reliably and efficiently exploit the potential of mathematical modeling and simulation of interacting particle systems.

Consortium and project goals

To this end, DATAHYKING unites researchers from 7 research institutes (KU Leuven, Università degli Studi di Ferrara, Università di Roma Sapienza, RWTH Aachen, Technische Universität Kaiserslautern, Université de Lille and INRIAi). This consortium will create a data-driven simulation framework for kinetic and hyperbolic models of interacting particle systems and define a common methodology for these future modeling and simulation experts. DATAHYKING will focus on:
– Developing reliable and efficient simulation methods;
– Designing robust consensus-based optimization, also for machine learning;
– Developing multifidelity methods for uncertainty quantification and data assimilation;
– Applications in traffic flow, finance, and granular flow, also in collaboration with industry.

The list of 5 available positions:

4. Forward uncertainty quantification for hyperbolic and kinetic equations
5. Robust consensus-based optimization for machine learning

8. Bayesian model calibration with uncertainty for traffic flow models

9. Advanced discretization methods for hyperbolic and kinetic equations with moving boundaries

11. Accelerated training methods for deep learning based on mean-field limits of neural ODEs

The other positions are already filled
More information and how to apply: please visit the website : https://datahyking.eu