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-cost indigenous wall materials: mud brick, clay-straw adobe, lime-stabilised bamboo panel, fired clay brick, and lime-mud composite. First, a validated Crank-Nicolson finite difference method (FDM) solves the one-dimensional transient heat equation with Robin boundary conditions under diurnal solar and outdoor air-temperature forcing, generating 1500 periodic-day solutions across a nine-dimensional parameter space by Latin Hypercube sampling. Second, a Physics-Informed Neural Operator (PINO) with a Fourier Neural Operator (FNO) backbone learns the parameter-to-solution operator mu ->T(x,t), enforcing both data fidelity and PDE consistency. The trained PINO attains a relative L2 field error of 5.14e-4 and a 0.201 K mean absolute error on the peak inner surface temperature, preserving the FDM material ranking exactly; PINO trained on 150 FDM samples matches a data-only FNO trained on twice as many, so the physics loss is most valuable when data are scarce. The periodic-day formulation also yields the ISO 13786 time lag and decrement factor, reproduced to within 0.99 h and 0.010. At nominal hot-dry summer conditions, clay-straw adobe achieves the best cost-performance index among widely available materials. A climate sweep, confirmed by FDM spot checks, reveals a regime boundary: under sub-ambient outdoor conditions the ranking inverts to conductive fired clay brick, delineating heat-exclusion and heat-rejection regimes. The framework supports evidence-based material selection for post-flood reconstruction in hot-dry regions.
Muhammad Akbar Khan, Fahim Raees, Ubaida Fatima· arXiv.org· 0 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 hyperparameter and found its optimum shifts by four orders of magnitude between rigid-body and deforming flows, but left open whether these principles transfer to three dimensions and whether single-seed results survive run-to-run variability. We answer both by repeating the weight selection across four 3D benchmarks (translating sphere, rotating sphere, slotted sphere, reversed vortex), sweeping six weights with three seeds at full training budget under a pre-registered selection rule. The ordering transfers: the selected weight tracks how far the exact solution departs from the signed-distance property, spanning four decades from $10^{-1}$ where it holds exactly to $10^{-5}$ where the interface is stretched. Values transfer only benchmark by benchmark; two of four carry over unchanged and two do not, so inheritance must be verified. The multi-seed protocol reveals that at small weights the seed-to-seed standard deviation equals the error itself, and the regulariser reduces it by more than an order of magnitude, buying reproducibility as well as accuracy. We benchmark against a fifth-order WENO solver on identical grids and error measures; the classical scheme is more accurate on all four problems, by two orders of magnitude on smooth rigid advection, with a margin that narrows with geometric difficulty and is smaller in volume conservation than in the field norm. Finally, we show that the relative $L_2$ error cannot certify the preservation of thin features, and report a feature-restricted measure that can.
Muhammad Akbar Khan· 0 citations
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