For the application of brain-computer interfaces in fields such as medicine, a method of classifying brain activity with high accuracy using small amount of training data is needed. To apply machine learning to biological signal processing, it is important to develop a method based on a model that matches the in vivo mechanism. While a high dimensional and high degree of freedom model can reproduce complex dynamics in a living body, it tends to overfit to the training data and may estimate activities that cannot exist in a living body when encountering novel data. Therefore, to improve the accuracy of classification and prediction, it is necessary to build a model that fits the nonlinearity and time delay of the neural population. In this study, we propose a machine learning method for the data from brain activity measurements by computing the time evolution of nodes in the reservoir computing network using the macroscopic neural population model. Since reservoir computing reproduces signals by linear summation of the time evolution of nodes, the outputs of the proposed method are limited to the waveforms that are based on the dynamics of the neuron population model. To verify the effect of the proposed method, the brain response to visual stimuli following a pseudorandom pattern was measured by magnetoencephalography, and the response of brain activities evoked by different stimulus patterns were estimated. The correlation coefficient between the measured waveform and the estimated waveform generated by the proposed method was higher than that of the conventional method. Comparison of individual node responses suggests that the non-linearity and time delay of the firing rate model, and the interaction between the excitatory and inhibitory neuronal populations contributed to the improvement in the adaptation to in vivo dynamics. Analytical approaches that incorporate knowledge of life phenomena for specialized machine learning models suitable for simulating biological phenomena will become more important in the future.