Physics-Informed Neural Networks for rarefied-gas dynamics: Poiseuille flow in the BGK approximation

Mario De Florio, Enrico Schiassi, Barry D. Ganapol, Roberto Furfaro

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


We present a new accurate approach to solving a class of problems in the theory of rarefied–gas dynamics using a Physics-Informed Neural Networks framework, where the solution of the problem is approximated by the constrained expressions introduced by the Theory of Functional Connections. The constrained expressions are made by a sum of a free function and a functional that always analytically satisfies the equation constraints. The free function used in this work is a Chebyshev neural network trained via the extreme learning machine algorithm. The method is designed to accurately and efficiently solve the linear one-point boundary value problem that arises from the Bhatnagar–Gross–Krook model of the Poiseuille flow between two parallel plates for a wide range of Knudsen numbers. The accuracy of our results is validated via the comparison with the published benchmarks.

Original languageEnglish (US)
Article number126
JournalZeitschrift fur Angewandte Mathematik und Physik
Issue number3
StatePublished - Jun 2022


  • Boltzmann equation
  • Extreme learning machine
  • Functional interpolation
  • Physics-Informed Neural Networks
  • Poiseuille flow
  • Rarefied gas dynamics

ASJC Scopus subject areas

  • Mathematics(all)
  • Physics and Astronomy(all)
  • Applied Mathematics


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