US Patent 7899657 Modeling in-situ reservoirs with derivative constraints

System and method for parameterizing one or more steady-state models each having a plurality of model parameters for mapping model input to model output through a stored representation of an in-situ hydrocarbon reservoir. For each model, training data representing operation of the reservoir is provided including input values and target output values. A next input value(s) and next target output value are received from the training data. The model is parameterized with the input value(s) and target output value, and derivative constraints imposed to constrain relationships between the input value(s) and a resulting model output value, using an optimizer to perform constrained optimization on the parameters to satisfy an objective function subject to the derivative constraints. The receiving and parameterizing are performed iteratively, generating a parameterized model. Multiple models form an aggregate model of the system/process, which may be optimized to satisfy a second objective function subject to operational constraints.