Violina: Various-of-trajectories Identification of Linear Time-invariant Non-Markovian Dynamics

We propose a new system identification method Violina (various-of-trajectories identification of linear time-invariant non-Markovian dynamics). In the Violina framework, we optimize the coefficient matrices of state-space model and memory kernel in the given space using a projected gradient descent method so that its model prediction matches the set of multiple observed data. Using Violina we can identify a linear non-Markovian dynamical system with constraints corresponding to a priori knowledge on the model parameters and memory effects. Using synthetic data, we numerically demonstrate that the Markovian and non-Markovian state-space models identified by the proposed method have considerably better generalization performances compared to the models identified by an existing dynamic decomposition-based method.