In this paper, we investigate the parameter identification problem in dynamical systems through a deep learning approach. Focusing mainly on second-order, linear time-invariant dynamical systems, the topic of damping factor identification is studied. By utilizing a six-layer deep neural network with different recurrent cells, namely GRUs, LSTMs or BiLSTMs; and by feeding input/output sequence pairs captured from a dynamical system simulator, we search for an effective deep recurrent architecture in order to resolve the damping factor identification problem. Our study's results show that, although previously not utilized for this task in the literature, bidirectional gated recurrent cells (BiLSTMs) provide better parameter identification results when compared to unidirectional gated recurrent memory cells such as GRUs and LSTM. Thus, indicating that an input/output sequence pair of finite length, collected from a dynamical system and when observed anachronistically, may carry information in both time directions to predict a dynamical systems parameter.