Connecting physio-chemical theory with electrical model is essential yet difficult for evaluating the impact of nonlinear ion transport on the performance of ionic circuits and electrochemical energy storage devices1-6. Here we demonstrate that machine learning can resolve this difficulty and produce physics-based nano-circuitry. Starting from a physio-chemical perspective, we first reveal an anomalous diffusion-enhanced migration of ions in nanopores, which exhibits a nonlinear electrical response. Using machine learning, we discover its underlying mathematical equation, and produce a dynamically varying ionic resistance for construction of nano-circuitry model. Based on the physio-chemical understanding of nano-circuitry model, we discover in supercapacitors that the nonlinear ion transport can lead to a Faradaic-like current peak in non-Faradaic processes and an asymmetric charging/discharging without ion desolvation, adding new perspectives to physio-chemistry.