CSQV 2025

Multiscale Model Learning in Computational Kinetic Theory

  • van Brummelen, Harald (Eindhoven University of Technology)
  • Abdelmalik, Michael (Eindhoven University of Technology)
  • Gieling, Bas (Eindhoven University of Technology)
  • Sharma, Revanth (Eindhoven University of Technology)
  • Shahine, Marwa (Eindhoven University of Technology)

Please login to view abstract download link

Kinetic theory describes fluid flows in terms of a particle probability distribution in position-velocity dependence. The theory is valid in the dilute/rarefied regime, i.e. if the distance between molecules is large relative to the characteristic length scales in the problem under consideration, but it also encapsulates all conventional macroscopic flow models such as the Navier-Stokes-Fourier equations in the so-called hydrodynamic limit, i.e. if the ratio of the mean free-path between molecules and characteristic length scales passes to zero. Kinetic theory owes this universality to its structural (conservation/dissipation) properties, notably conservation of mass, momentum and energy and entropy dissipation. These properties are also fundamental to stability of the equations. The details of molecular interactions in kinetic theory are encoded in the so-called collision operator. To enhance the descriptive capabilities of the collision operator, it can be learned from an underlying microscopic model such as molecular dynamics, and encoded in a neural net. The neural net then acts as a multiscale model, bridging between MD and kinetic theory. However, standard learning procedures do not retain the fundamental structural properties, or only do so in an average sense, and thus lead to unstable equations or incorrect limits. In the presentation I will elaborate how ML can be used in computational kinetic theory (CKT) while upholding the structural properties of the equations. I will also share some personal insights into the role of ML in CKT and CSE in general.