Problem in minimizing functional for 4D Variationa Data Assimilation


I’m implementing a variational data assimilation approach in time on a 3D space to combine 4D flow measurments of blood flow in a cerebral aneurysm and Navier-Stokes solutions to recover optimal inlet boundary conditions following the work () published by S. Funke and co-workers.
However, for couple of weeks I have been stuck in solving the optimization problem (solved by a L-BFGS method) through the minimization library provided by scipy. It seems that my functional is not well-defined since the line-search method is not able to find a descent direction in 20 iterations (basically, I got this error message [ABNORMAL_TERMINATION_IN_LNSRCH]).
As reported in the work provided by S. Funke, my fuctional J is defined only at the time instants where blood velocity measurments occurs, as mismatch between the velocity obtained in my forward passage and the measurments, normalized with L2 norm. I add some regularization term for my control (the inlet boundary condition) defined for all the period of my simulation. I have checked evral time the formulation of my function and it looks fine for me. If I correctly understood this type of problem can happen when the “shape” of the functional is too flat and global minima are hard to be found.

For this reason, I would like to get from you guys some tips which can help to solve this type of problem.

Thanks in advance,