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UID:submissions.pasc-conference.org_PASC24_sess180_pap104@linklings.com
SUMMARY:Towards Sobolev Pruning
DESCRIPTION:Paper\n\nNeil Kichler, Sher Afghan, and Uwe Naumann (RWTH Aach
 en University)\n\nThe increasing use of stochastic models for describing c
 omplex phenomena warrants surrogate models that capture the reference mode
 l characteristics at a fraction of the computational cost, foregoing poten
 tially expensive Monte Carlo simulation. The predominant approach of fitti
 ng a large neural network and then pruning it to a reduced size has common
 ly neglected shortcomings. The produced surrogate models often will not ca
 pture the sensitivities and uncertainties inherent in the original model. 
 In particular, (higher-order) derivative information of such surrogates co
 uld differ drastically. Given a large enough network, we expect this deriv
 ative information to match. However, the pruned model will almost certainl
 y not share this behavior.<br /><br />In this paper, we propose to find su
 rrogate models by using sensitivity information throughout the learning an
 d pruning process. We build on work using Interval Adjoint Significance An
 alysis for pruning and combine it with the recent advancements in Sobolev 
 Training to accurately model the original sensitivity information in the p
 runed 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 prop
 osed method is, however, not limited to the domain of quantitative finance
 , which was chosen as a case study for intuitive interpretations of the se
 nsitivities. It serves as a foundation for building further surrogate mode
 lling techniques considering sensitivity information.\n\nDomain: Computati
 onal Methods and Applied Mathematics\n\nSession Chair: Luca Muscarnera (Po
 litecnico di Milano)
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