With rapid advancements in materials science, new materials are emerging constantly. It is important to characterize the mechanical properties of new materials to guide their application and design. In this study, a parameter calibration method assisted by machine learning is proposed to quickly and accurately obtain the parameters of constitutive models of materials. A physics-informed neural network (PINN) with an embedded constitutive model is constructed. The PINN outputs elastic strain, plastic strain, and stress. The loss function incorporates both elastic and plastic constitutive models, with the constitutive parameters set as trainable variables. This approach allows the network to automatically adjust these parameters during training. The finite element method is applied to simulate published quasi-static and dynamic compression experiments on materials to enrich a dataset of response curves and constitutive parameters. The dataset, composed of 1600 numerical examples and nearly 100 published experimental results, is used to test the method. By fine-tuning the network structure, the data-driven neural network solution was able to achieve an accuracy of 93% on the test set. Compared to the traditional data processing methods, the time spent using this method for parameter identification is reduced to one percent of the conventional duration, significantly improving the working efficiency. A calibration method assisted by machine learning shows great potential in quickly obtaining a mechanical constitutive model of materials, avoiding the waste of human resources and preventing human-induced errors.