Abstract: A method for preferential system identification (PSID) for modeling neural dynamics of a brain includes extracting behaviorally relevant latent brain states via a projection of future behavior onto past neural activity. The method further includes identifying, based on the extracted latent brain states, model parameters for a linear state space dynamic model of neural activity. An extension of PSID includes accounting for an effect of external inputs to the brain by using oblique projections along the external inputs instead of orthogonal projections. PSID may be extended to apply to any primary signals and secondary signals in place of the neural activity and the behavior. In some embodiments, the extracting and the identifying may be performed using a numerical optimization of recurrent neural networks (RNN) instead of the projection.