Spatio-Temporal Gradient Enhanced Surrogate Modeling Strategies

This research compares the performance of space-time surrogate models (STSMs) and network surrogate models (NSMs). Specifically, when the system response varies over time (or pseudo-time), the surrogates must predict the system response. A surrogate model is used to approximate the response of computationally expensive spatial and temporal fields resulting from some computational mechanics simulations. Within a design context, a surrogate takes a vector of design variables that describe a current design and returns an approximation of the design's response through a pseudo-time variable. To compare various radial basis function (RBF) surrogate modeling approaches, the prediction of a load displacement path of a snap-through structure is used as an example numerical problem. This work specifically considers the scenario where analytical sensitivities are available directly from the computational mechanics' solver and therefore gradient enhanced surrogates are constructed. In addition, the gradients are used to perform a domain transformation preprocessing step to construct surrogate models in a more isotropic domain, which is conducive to RBFs. This work demonstrates that although the gradient-based domain transformation scheme offers a significant improvement to the performance of the space-time surrogate models (STSMs), the network surrogate model (NSM) is far more robust. This research offers explanations for the improved performance of NSMs over STSMs and recommends future research to improve the performance of STSMs.