Operators for interfacial problems are trained on reference solutions produced by the solver they are intended to replace. This work develops a data-free physics-informed neural operator for level-set interface advection, in which the interface is the equation's unknown and the operator maps an initial interface to the...
This work shows that standard gradient-norm balancing fails, and introduces SDF-Aware Weighting (SAW), which combines a residual-quantile gate with a gradient-norm ratio so that points exhibiting legitimate departure are excluded before the surviving term is scaled.
Identifying cost-effective indigenous building materials that minimise heat penetration through walls is critical for indoor thermal comfort in low-income rural housing in hot-dry climates, where summer temperatures routinely exceed 45 C. We present a two-stage computational framework for thermal ranking of five low-co...
Muhammad Akbar Khan, Fahim Raees, Ubaida Fatima· arXiv.org· 0 citations
A key finding is an RFF–eikonal joint design constraint: at low bandwidth, weak eikonal regularization distorts the signed-distance field and underperforms the tanh baseline, whereas higher bandwidth is compatible with moderate regularization and yields the global best result.
Muhammad Akbar Khan, Fahim Raees· Machine Learning: Science an...· 2 citations
Physics-informed neural networks applied to the level-set formulation of interface advection commonly augment the residual and initial-condition losses with an eikonal regulariser, penalising the deviation of $\|\nabla\phi\|$ from unity. A previous two-dimensional study identified this weight as the dominant hyperparam...
Muhammad Akbar Khan· 0 citations
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