The precise knowledge of the hydraulic pressure losses while drilling is one of the crucial factors for the success of the entire drilling process. The pump must operate providing the desired flow rate necessary for e.g. hole cleaning requirements and should do that within a predictable and accurate pressure range. The operating pressure is thereby concurrently limited by pipe and equipment constraints. Pore pressure, formation fracture gradients and resulting maximum allowable equivalent circulating density introduce additional complexity to the hydraulic system. However, taking the complete drilling system under consideration, severe challenges arise in representing the reality for pump pressure prediction due to the restricted knowledge of several relevant parameters at any given point in time. This work demonstrates a method for simulating drilling hydraulics, applicable in real-time, as well as during the planning phase. The proposed method combines deterministic with non-linear heuristic approaches. The deterministic approaches are based on classical rheological models incorporating fluid properties, borehole geometry, casing and drill string configuration as well as detailed information regarding the well path. Although the deterministic approaches work well when all input parameters of the model are well defined and known, in real-world applications a lack of accuracy is caused by several uncertainties: mud properties change with temperature and pressure along the flow path thru the wellbore; the relative roughness of the borehole wall, as well as the borehole diameter in open holes is typically not known as some examples. To tackle those unknowns and their non-linear impact on results, the classical models have been extended by data driven models, namely neural networks. Based on real-time sensor measurements, those extended models were trained for simulating the standpipe pressure on both, single and multi-well scenarios. Furthermore, the concept has been extended by the addition of automated operation recognition results, allowing the variety of different operational states to influence the creating of individual state driven models for hydraulic analysis. Finally, in order to meet the current requirements for a drilling hydraulics simulator, the results are presented in a clear and understandable interface, ensuring a detailed real-time wellbore hydraulic overview, including equipment and formation pressure limitations as well hole cleaning requirements.