Some questions about surrogate model accelerate Bayesian inference

Dear uqlab team:
Many thanks to uqlab for the great convenience of my research work.
I have two question about the Bayesian inverse:

Q1: Can this example uq_Example_Inversion_08_Surrogate directly generate a graph(like the below) of the iterative process for the objective function?

Q2:Can we put aside the optimization algorithm and directly use the inverse modeling of the surrogate model to predict the corresponding output (the original unknown input parameters) by taking the actual measured data as the known input?
The optimization algorithm is essentially an iterative search for the optimal solution, and its ultimate goal is to find an extreme value point as close as possible to the actual data point.I think the unknown input parameters predicted by directly using the inverse modeling of the surrogate model are very close to the results obtained by adding the optimization algorithm.

Thank you very much!

hi,@Olaf Klein ,I hope you can give some valuable advice, thank you very much!