Tuning coils based on the magnetic field map in COMSOL

Recently I am replicating a multi-solenoid coil system that the internal and external map of the magnetic field known.

Since the inner field is known, the currents in the coils are ‘predicted’ based on the biot-savart law. So, predicted current numbers enable the magnetic field as expected IN the magnet but the external field was wrong (overestimated). Now I am thinking the other way around, and predicting the currents in the coils based on multiple points of the (external and the internal) magnetic field.

As a not-professional COMSOL user, wonder if this is possible. I would like to hear some suggestions or ideas to predict the currents that provide the magnetic field as expected.