  In this paper we present the work related to the parameters identification
for Abrasive Waterjet Milling (AWJM) model that appears as an ill-posed inverse
problem. The necessity of studying this problem comes from the industrial
milling applications where the possibility to predict and model the final
surface with high accuracy is one of the primary tasks in the absence of any
knowledge of the model parameters that should be used. The adjoint approach
based on corresponding Lagrangian gives the opportunity to find out the
unknowns of the AWJM model and their optimal values that could be used to
reproduce the required trench profile. Due to the complexity of the nonlinear
problem and the large number of the model parameters, we use an automatic
differentiation (AD) software tool. This approach also gives us the ability to
distribute the research on more complex cases and consider different types of
model errors and 3D time dependent model with variations of the jet feed speed.
This approach gives us a good opportunity to identify the optimal model
parameters and predict the surface profile both with self-generated data and
measurements obtained from the real production. Considering different types of
model errors allows us to receive the results acceptable in manufacturing and
to expect the proper identification of unknowns.
