Enhancing Polynomial Chaos Expansion Based Surrogate Modeling using a
  Novel Probabilistic Transfer Learning Strategy
Wyatt Bridgman Uma Balakrishnan Reese Jones Jiefu Chen Xuqing Wu Cosmin Safta Yueqin Huang Mohammad Khalil
In the field of surrogate modeling, polynomial chaos expansion (PCE) allows
practitioners to construct inexpensive yet accurate surrogates to be used in
place of the expensive forward model simulations. For black-box simulations,
non-intrusive PCE allows the construction of these surrogates using a set of
simulation response evaluations. In this context, the PCE coefficients can be
obtained using linear regression, which is also known as point collocation or
stochastic response surfaces. Regression exhibits better scalability and can
handle noisy function evaluations in contrast to other non-intrusive
approaches, such as projection. However, since over-sampling is generally
advisable for the linear regression approach, the simulation requirements
become prohibitive for expensive forward models. We propose to leverage
transfer learning whereby knowledge gained through similar PCE surrogate
construction tasks (source domains) is transferred to a new
surrogate-construction task (target domain) which has a limited number of
forward model simulations (training data). The proposed transfer learning
strategy determines how much, if any, information to transfer using new
techniques inspired by Bayesian modeling and data assimilation. The strategy is
scrutinized using numerical investigations and applied to an engineering
problem from the oil and gas industry.