Time series causal discovery is key to understanding causal mechanisms among variables in dynamic systems. However, most of the previous causal discovery methods implicitly assume the inability to incorporate expert domain knowledge, which limits the effectiveness of their application to some extent. In this paper, we propose a score-based nonparametric structural learning method, NOTEARS-cMLP, specifically for time series data to accurately discover instantaneous and lagged causal relationships among variables. The NOTEARS- cMLP method uses cMLP to simulate nonlinear dependencies among time series variable relationships and incorporates NOTEARS ideas to describe causal structure learning as a continuous optimization problem with acyclic constraints. In addition, the method further improves the accuracy and efficiency of dependency identification by incorporating do-main knowledge as a constraint into the L-BFGS-B optimization algorithm. Empirical evaluations of simulated data demonstrate the effectiveness and robustness of the NOTEARS- cMLP for the learning of DAGs, and an applied study on the attribution of gold futures trading prices is conducted.