To accurately model 4H-SiC MOSFETs over a wide temperature operating range, this work proposes a compact modeling method based on physically informed artificial neural networks(ANNs). The method relies on two independent ANNs, the first ANN is based on the symmetry-modified BSIM model, which is used to predict the main trends of the I-V curves. The second ANN is used to train a model correction function related to non-ideal factors not covered in the above model. This method is able to ensure the symmetry requirements of the model even without adding a smoothing function. The introduction of physical information allows the model to accurately predict the I-V characteristics of the MOSFET and guarantee the smoothness of its derivatives. A major advantage is that less than 30% of the data is needed to achieve the same model accuracy as ANN without physical information. We have simulated the designed device models in Spice software for E/E saturated load NMOS inverters and NAND logic circuits, and the results show that the maximum model error does not exceed 1.8%.