A two-branch physics-informed neural network for small-sample sedimentation prediction of magnetorheological fluids

Sedimentation tests of magnetorheological fluids (MRFs) under natural gravity are time-consuming, limiting the experimental coverage of particle concentrations and formulations. This study proposes a moving-boundary data-interpolated physics-informed network (MB-DIP) to jointly predict concentration-field evolution and mudline motion from a limited number of measured source samples and the known initial state of a target sample. The two-branch architecture combines a physical mudline prior with a moving-boundary-aligned concentration-field prior. Conservation-constrained field refinement and reliability-guided interface consistency refinement subsequently coordinate local particle transport, overall particle content, and interface motion. For baseline MRFs, samples with initial particle volume fractions of 7.5, 10, 15, and 32 vol% were used to predict sedimentation at 20 and 26 vol%. The mean absolute errors of the concentration field and mudline position were 2.04% and 1.96 mm, respectively, and the mean absolute percentage error of particle content was 2.83%. Ablation experiments demonstrated the contribution of physics-consistency refinement, while six-fold leave-one-source-concentration-out validation examined prediction performance under varying source-data coverage. Further validation used SiO₂-modified MRFs containing 28 vol% carbonyl iron particles and 0.25–1 wt% silica. MB-DIP captured changes in sedimentation behavior with silica content, whereas the theoretical predictions remained unchanged. Concentration-field and mudline mean absolute errors ranged from 0.620% to 1.872% and from 0.306 to 1.081 mm, respectively. These results support MB-DIP as a method for predicting MRF sedimentation under limited-data conditions, with potential to reduce the experimental effort required for formulation evaluation.