•A neural network is developed as a surrogate tool fed by a numerical dataset.•PSO utilizes monitoring data to estimate most probable rheological parameters.•The methodology is validated on two adjacent tunnels in karstic rock mass.•Numerical results agreed well with the long-term monitored settlements. The continuous monitoring of long-term performance of tunnels constructed in soft rock masses shows that the rock mass deformations continue after construction, albeit at a rate that reduces with time. This is in contrast with NATM postulates which assume deformation stabilizes shortly after tunnel construction. This paper proposes the prediction of long-term vertical settlement performance of a tunnel in soft rock mass, through the inclusion of a Burger’s creep viscous-plastic constitutive law to model post-construction deformations. To overcome issues related to the complex characterization of this constitutive model, a neural network NetRHEO is developed and trained on a numerically obtained dataset. A particle swarm algorithm is then employed to estimate the most probable rheological parameter set, by utilizing the long-term in-situ monitoring data from several observation points on a real tunnel. The paper demonstrates the potential of the proposed methodology, using displacement measurements of two adjacent tunnels in karstic rock mass in Croatia. The complex interaction of a railway tunnel Brajdica and a road tunnel Pećine, conditioned by the character of the surrounding rock mass as well by the chronology of their construction, was evaluated to predict the future behavior of these tunnels.