A machine learning strategy for computing interface curvature in Front-Tracking methods

Error-Correcting Neural Networks for Two-Dimensional Curvature Computation in the Level-Set Method

“…This idea [39,68,69] could free us from hand-tuning hκ * min in Algorithms 1 to 3 and possibly hκ up min in the MLCurvature() function. Lastly, we could include data from neighboring interface nodes, analogous to [40], but as analytical constraints [70]. This way, we could enforce some smoothness and reduce sharp curvature variations between "successive" nodes.…”

“…Their ML solution has worked well for under-resolved regions while preserving the numerical convergence around well-resolved sectors. Also, Franc ¸a and Oishi [40] have recently introduced a neural strategy motivated by [33] for calculating curvature in front-tracking. Their multilayer perceptrons [34,35] simply consume normal-and tangential-vector angles to emit curvature estimates at the marker points.…”

Hybridization of front tracking and level set for multiphase flow simulations: a machine learning approach

“…Data-driven strategies have recently shown their powerful ability across diverse fields including the fluid mechanics communities [10,11], and a few attempts introducing machine-learning (ML) techniques have also appeared in multiphase flow simulation fields. Qi et al [12], Larios-Cárdenas and Gibou [13], and Franca and Oishi [14] utilized ML strategies to compute the interface curvature for volume of fluid (VOF), level set (LS), and front tracking (FT) simulations, respectively. Ataei et al [15] also used ML to replace the conventional iterative computation for the piecewise linear interface construction (PLIC) in VOF simulation.…”

“…Ataei et al [15] also used ML to replace the conventional iterative computation for the piecewise linear interface construction (PLIC) in VOF simulation. Although a very few studies are available in literature and those are still at initial stages, they have demonstrated the potential of ML strategies in multiphase flow simulations [12][13][14][15].…”

Machine Learning Algorithms for Three-Dimensional Mean-Curvature Computation in the Level-Set Method

“…Like these, there have been other contemporary deep learning implementations devoted to solving geometrical difficulties in conventional numerical schemes. These include, for instance, the curvature prediction from angular and normal-vector information [50] in front-tracking and the neural calculation of linear piecewise interface construction (PLIC [51]) coefficients [52] in the VOF method. Likewise, one can find advancements in the level-set framework, such as Buhendwa, Bezgin, and Adams' consistent algorithms for inferring area fractions and apertures for IR [53].…”