Wyatt Bridgman

Wyatt Bridgman, Uma Balakrishnan, Reese Jones et al.

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.

Wyatt Bridgman, Xiaoxuan Zhang, Greg Teichert et al.

In this work we employ an encoder-decoder convolutional neural network to predict the failure locations of porous metal tension specimens based only on their initial porosities. The process we model is complex, with a progression from initial void nucleation, to saturation, and ultimately failure. The objective of predicting failure locations presents an extreme case of class imbalance since most of the material in the specimens do not fail. In response to this challenge, we develop and demonstrate the effectiveness of data- and loss-based regularization methods. Since there is considerable sensitivity of the failure location to the particular configuration of voids, we also use variational inference to provide uncertainties for the neural network predictions. We connect the deterministic and Bayesian convolutional neural networks at a theoretical level to explain how variational inference regularizes the training and predictions. We demonstrate that the resulting predicted variances are effective in ranking the locations that are most likely to fail in any given specimen.