A large-scale, general-purpose data assimilation (DA) platform for materials modeling, douka, was developed and applied to nonlinear materials models. The platform demonstrated its effectiveness in estimating physical properties that cannot be directly obtained from observed data. Furthermore, it enables state estimation with quantified uncertainty, thereby providing researchers with a new aspect for analyzing the underlying physical process and guiding future model refinements. DA was successfully performed using experimental images of oxygen evolution reaction at a water electrolysis electrode, enabling the estimation of oxygen gas injection velocity and bubble contact angle. Furthermore, large-scale ensemble DA was conducted on the supercomputer Fugaku, achieving state estimation with up to 8192 ensemble members. The results confirmed that runtime scaling for the prediction step follows the weak scaling law, ensuring computational efficiency even with increased ensemble sizes. These findings highlight the potential of douka as a new approach for data-driven materials science, integrating experimental data with numerical simulation.