Methods and systems for characterizing hydraulic fracturing of a subterranean formation based upon inputs from sensors measuring field data in conjunction with a fracture model. Such characterization can be generated in real-time to automatically manipulate surface and/or down-hole physical components supplying hydraulic fluids to the subterranean formation to adjust the hydraulic fracturing process as desired. The hydraulic fracture model as described herein can also be used as part of forward calculations to help in the design and planning stage of a hydraulic fracturing treatment. In a preferred embodiment, the fracture model constrains geometric and geomechanical properties of the hydraulic fractures of the subterranean formation using the field data in a manner that significantly reduce the complexity of the fracture model and thus significantly reduces the processing resources and time required to provide accurate characterization of the hydraulic fractures of the subterranean formation.