Abstract: Machine learning is an effective method for flow representation. Data-driven machine learning models lack the interpretability of physical mechanisms, and it is difficult to obtain accurate models when there are few training samples available. An artificial neural network model using flow time history data of measurement point is proposed. The output of the model is further improved using flow governing equations, resulting a machine learning model of the flow time history considering physical constraints. The neural network model is proposed to represent the flow time history data at different locations, and the model is trained with known measurement point samples; then the model output is used to calculate the loss of the Naïve-stokes equations to improve the purely data-driven model parameters. The model is verified using flow time history data around square cylinder at low Reynolds number, and it is demonstrated that the physical constraint method can improve the accuracy of the results. The method proposed in this paper is applicable to the analysis of flow data based on measurement points, and the model accuracy is improved by introducing constraints on the flow governing equations, making the model more accurate and more consistent with the physical laws for the flow time history representation with limited available measurement data.