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.

本文提出了一种新的系统识别方法Violina，旨在解决线性时间不变非马尔可夫动态模型识别中存在的问题。该方法通过投影梯度下降法优化状态空间模型的系数矩阵和记忆核，从而使模型预测与多个观察数据集相匹配。实验结果表明，与现有方法相比，Violina在识别线性非马尔可夫动态系统时具有显著更好的泛化性能。

Violina：线性时间不变非马尔可夫动态的多轨迹识别