Pursuit of hidden rules behind the irregularity of nano capillary lithography by hybrid intelligence

Nature finds a way to leverage nanotextures to achieve desired functions. Recent advances in nanotechnologies endow fascinating multi-functionalities to nanotextures by modulating the nanopixel's height. But nanoscale height control is a daunting task involving chemical and/or physical processes. As a facile, cost-effective, and potentially scalable remedy, the nanoscale capillary force lithography (CFL) receives notable attention. The key enabler is optical pre-modification of photopolymer's characteristics via ultraviolet (UV) exposure. Still, the underlying physics of the nanoscale CFL is not well understood, and unexplained phenomena such as the "forbidden gap" in the nano capillary rise (unreachable height) abound. Due to the lack of large data, small length scales, and the absence of first principles, direct adoptions of machine learning or analytical approaches have been difficult. This paper proposes a hybrid intelligence approach in which both artificial and human intelligence coherently work together to unravel the hidden rules with small data. Our results show promising performance in identifying transparent, physics-retained rules of air diffusivity, dynamic viscosity, and surface tension, which collectively appear to explain the forbidden gap in the nanoscale CFL. This paper promotes synergistic collaborations of humans and AI for advancing nanotechnology and beyond.