Performance and stability of physics-informed Kolmogorov-Arnold networks for two-phase transport in porous media: A comparative study with physics-informed neural networks
Imankulov T. Kenzhebek Y. Bekele S.D. Akhmed-Zaki D.
March 2026Elsevier B.V.
Results in Engineering
2026#29
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 2592 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 (1140 vs. 3462), but consistently requires a larger artificial diffusion coefficient to suppress training-time oscillations at the shock front (εPIKAN=0.00575 vs. εPINN=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.
Artificial diffusion , Buckley-Leverett equation , Hyperbolic conservation laws , Kolmogorov-Arnold networks , Physics-informed neural networks , Porous media flow
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Al-Farabi Kazakh National University, Almaty, 050040, Kazakhstan
Mukhtar Auezov South Kazakhstan University, Shymkent, 160012, Kazakhstan
Al-Farabi Kazakh National University
Mukhtar Auezov South Kazakhstan University
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026