  The increasing use of stochastic models for describing complex phenomena
warrants surrogate models that capture the reference model characteristics at a
fraction of the computational cost, foregoing potentially expensive Monte Carlo
simulation. The predominant approach of fitting a large neural network and then
pruning it to a reduced size has commonly neglected shortcomings. The produced
surrogate models often will not capture the sensitivities and uncertainties
inherent in the original model. In particular, (higher-order) derivative
information of such surrogates could differ drastically. Given a large enough
network, we expect this derivative information to match. However, the pruned
model will almost certainly not share this behavior.
  In this paper, we propose to find surrogate models by using sensitivity
information throughout the learning and pruning process. We build on work using
Interval Adjoint Significance Analysis for pruning and combine it with the
recent advancements in Sobolev Training to accurately model the original
sensitivity information in the pruned neural network based surrogate model. We
experimentally underpin the method on an example of pricing a multidimensional
Basket option modelled through a stochastic differential equation with Brownian
motion. The proposed method is, however, not limited to the domain of
quantitative finance, which was chosen as a case study for intuitive
interpretations of the sensitivities. It serves as a foundation for building
further surrogate modelling techniques considering sensitivity information.
