WIAS Preprint No. 3134, (2024)

Bound-preserving PINNs for steady-state convection-diffusion-reaction problems


Authors

  • John, Volker
    ORCID: 0000-0002-2711-4409
  • Matthaiou, Marina
  • Zainelabdeen, Marwa

2020 Mathematics Subject Classification

  • 65N99 68T07

Keywords

  • Steady-state convection-diffusion-reaction problems, convection-dominated regime, PINNs, bound-preservation

DOI

10.20347/WIAS.PREPRINT.3134

Abstract

Numerical approximations of solutions of convection-diffusion-reaction problems should take only physically admissible values. Provided that bounds for the admissible values are known, this paper presents several approaches within PINNs and $hp$-VPINNs for preserving these bounds. Numerical simulations are performed for convection-dominated problems. One of the proposed approaches turned out to be superior to the other ones with respect to the accuracy of the computed solutions.

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