Performance and stability of physics-informed Kolmogorov-Arnold networks for two-phase transport in porous media: A comparative study with physics-informed neural networks

• 2,592-run sensitivity study of PIKANs on Buckley-Leverett shocks • PIKAN achieve comparable accuracy to PINNs with 3 × fewer parameters (1,140 vs 3,462) • PIKAN needs stronger artificial diffusion than PINN (0.00575 vs 0.0025) • Optimal PIKAN depends on metric: L 2 / W 1 favor simple, H 1 / E favor complex • Spline order and knot density dominate PIKAN accuracy and stability We present the first large-scale sensitivity and comparative study of Physics-Informed Kolmogorov–Arnold Networks (PIKAN) for a two-phase transport problem in porous media, using the Buckley–Leverett equation as a canonical benchmark. Across 2,592 distinct configurations on the canonical Buckley–Leverett problem, we map the PIKAN performance landscape and quantify an empirical stability–parameter efficiency trade-off under a fixed strong-form training setup: in our experiments, an optimised PIKAN achieves error levels of the same order as a classical Physics-Informed Neural Network (PINN) while using nearly three times fewer parameters (1,140 vs. 3,462), but consistently requires a larger artificial diffusion coefficient to suppress training-time oscillations at the shock front ( ε PIKAN = 0.00575 vs. ε PINN = 0.0025 ). Using four complementary metrics: the L 2 relative error, H 1 seminorm, energy norm E , and Wasserstein-1 distance W 1 , we show that the optimal PIKAN architecture is metric-dependent: simpler, low-order models best capture global solution structure ( L 2 , W 1 ), whereas higher-order, dense-knot models are needed to resolve physical gradients ( H 1 , E ). Our experiments span controlled sweeps of depth, width, spline order, and knot density under common collocation grids and four evaluation times. We also report parameter counts, wall-clock convergence, and reproducibility with fixed seeds. Analysis via feature-importance isolates spline order and knot density as primary drivers of performance. Within the Buckley–Leverett setting, these results make the trade-off explicit between parameter count and stabilization strength and provide metric-aware guidance for selecting PIKAN architectures.