Bioceramics, such as hydroxyapatite and β-tricalcium phosphate, are widely used in orthopedics and oral surgery because they are free in shape and size and are not harvested from patients or donors. General development of bioceramics requires a great deal of effort, a long time, and many animal experiments. Because an animal experiment takes several months and is currently regarded as an ethical problem, the number of experiments should be reduced. In this study, machine learning was applied to construct mathematical models to predict the material properties, including the porosity, compressive strength, Ca2+ dissolution rate, and bone formation rate, from the synthesis conditions and to design synthesis conditions of bioceramics with desired bone formation rates. We propose two types of models: model 1 to predict the material properties, crystallite sizes, and second selected Fourier transform infrared wavenumbers of the resulting bioceramics from the synthesis conditions, such as the starting powder conditions, and model 2 to predict the bone formation rate from the material properties, crystallite sizes, second selected Fourier transform infrared wavenumbers, and animal experimental conditions of bioceramics. Both models were constructed using Gaussian mixture regression, enabling direct inverse analysis of the models. Furthermore, by visualization of the models, the relationships among the bone formation rate, material properties, and animal experimental conditions can be understood to establish guidelines for designing the synthesis conditions. We succeeded in designing artificial bone synthesis conditions with bone formation rate exceeding existing bone formation rates.