An adaptive learning strategy for surrogate modeling of high-dimensional functions - Application to unsteady hypersonic flows in chemical nonequilibrium

Many engineering applications rely on the evaluation of expensive, non-linear high-dimensional functions. In this paper, we propose the RONAALP algorithm (Reduced Order Nonlinear Approximation with Adaptive Learning Procedure) to incrementally learn, on-the-fly as the application progresses, a fast and accurate reduced-order surrogate model of a target function. First, a combination of nonlinear auto-encoder, community clustering, and radial basis function networks allows us to learn an efficient and compact surrogate model with limited training data. Secondly, an active learning procedure overcomes any extrapolation issues during the online stage by adapting the surrogate model with high-fidelity evaluations that fall outside its current validity range. This approach results in generalizable, fast, and accurate reduced-order models of high-dimensional functions. The method is demonstrated on three direct numerical simulations of hypersonic flows in chemical nonequilibrium. Accurate simulations of these flows rely on detailed thermochemical gas models that dramatically increase the cost of such calculations. Using RONAALP to learn a reduced-order thermodynamic model surrogate on-the-fly, the cost of such simulations was reduced by up to 75% while maintaining an error of less than 10% on relevant quantities of interest.