Intelligence Across Scales to Guide Innovations

This paper introduces Scaled-cPIKAN, a physics-informed architecture rooted in Kolmogorov-Arnold Networks (KANs). Scaled-cPIKAN integrates Chebyshev polynomial representations with a domain scaling approach that transforms spatial variables in residual PDEs into the standardized domain [‑1, 1]^d, as intrinsically required by Chebyshev polynomials.

This study aims to investigate the effects of discontinuous wettability on droplet breakup structures under microgravity conditions using a microchannel wall. The approach we adopt is underpinned by the volume-of-fuid methodology, an efficient technique renowned for its accurate resolution of the fuid interface in a two-phase flow.