A non-Newtonian dam break experiment is inversely simulated with the moving particle hydrodynamics (MPH) method by adapting physical parameters via the Bayesian optimization. Because of the physical consistency, which is asserted when the discrete system satisfies the fundamental laws of physics, the MPH method for incompressible flows (MPH-I) can robustly calculate wide range of viscosity without empirical parameter tuning. This feature was helpful in optimization process because the trial cases with various parameters could unconditionally be calculated stably. Specifically, the history of the front edge position could be reproduced with optimizing yield stress and plastic viscosity in the bi-linear Bingham model.