The transformation and transmission of brain stimuli reflect the dynamical brain activity in space and time. Compared with functional magnetic resonance imaging (fMRI), magneto- or electroencephalography (M/EEG) fast couples to the neural activity through generated magnetic fields. However, the MEG signal is inhomogeneous throughout the whole brain, which is affected by the signal-to-noise ratio, the sensors’ location and distance. Current non-invasive neuroimaging modalities such as fMRI and M/EEG excel high resolution in space or time but not in both. To solve the main limitations of current technique for brain activity recording, we propose a novel recurrent memory optimization approach to predict the internal behavioral states in space and time. The proposed method uses Optimal Polynomial Projections to capture the long temporal history with robust online compression. The training process takes the pairs of fMRI and MEG data as inputs and predicts the recurrent brain states through the Siamese network. In the testing process, the framework only uses fMRI data to generate the corresponding neural response in space and time. The experimental results with Human connectome project (HCP) show that the predicted signal could reflect the neural activity with high spatial resolution as fMRI and high temporal resolution as MEG signal. The experimental results demonstrate for the first time that the proposed method is able to predict the brain response in both milliseconds and millimeters using only fMRI signal.