Inferring surface slip in active colloids from flow fields using physics-informed neural networks

The directed motion of active colloids is governed by spatial variations in surface chemistry that generate effective interfacial flows, yet the resulting slip distributions remain extremely difficult to measure directly. We introduce a physics-informed neural network framework that infers the slip distribution driving propulsion from partial observations of the surrounding flow. By combining partial fluid-velocity measurements with the Stokes equations and boundary constraints, the method reconstructs both the near-surface slip and the full velocity field. Validation against analytical solutions and boundary element method calculations for canonical active colloid models shows quantitative agreement in both unbounded and confined geometries. Systematic tests identify the conditions under which the reconstruction degrades as measurement availability decreases or noise increases, while comparison with radial-basis-function interpolation demonstrates the importance of the governing equations for recovering the data-free near-surface flow. Crucially, the framework recovers the surface slip even when no flow data are available near the particle, demonstrating that accessible bulk measurements encode the effective surface slip associated with active motion.