Deep Capsule Encoder-Decoder Network for Surrogate Modeling and Uncertainty Quantification

The lack of complete knowledge about a system in mechanics or some randomness intrinsic to the system leads to emergence of uncertainty in numerical simulators. In order to ascertain the effect of such uncertainty on the output of a numerical simulators, it is essential that one looks towards the field of uncertainty quantification [1]. More precisely, it is only relevant the problem under consideration be reformulated into an uncertainty propagation (UP) problem. The most straightforward way to solve UP problem is via the usage of Monte Carlo (MC) method [2], which requires considerably large number of repeated evaluation of the solution of the problem at random input samples for getting convergent statistics. Now, of course, if we take into account the high computational cost of a single simulation run for complex multiscale and multiphysics systems, the situation becomes even more daunting and expensive for repeated evaluations. Furthermore, even the more advanced techniques such as Latin Hypercube Sampling [3] and Quasi MC-method [4] do not come to rescue and are often not apt for UP problems. Therefore, in such scenarios, the rational choice is to construct computationally efficient surrogate models (SM) which could then be queried instead of the original simulator using sampling methods such as the MC-method for completing UQ tasks. Further, some of the notable approaches for surrogate constructions in literature include polynomial chaos expansion [5, 6, 7], Gaussian processes [8, 9, 10, 11], variance decomposition analysis [12, 13] and its variants [14], support vector machines [15], and deep neural networks [16, 17, 18, 19, 20, 21].