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

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.