  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 Active Learning Procedure) to
incrementally learn a fast and accurate reduced-order surrogate model of a
target function on-the-fly as the application progresses. First, the
combination of nonlinear auto-encoder, community clustering and radial basis
function networks allows to learn an efficient and compact surrogate model with
limited training data. Secondly, the active learning procedure overcome any
extrapolation issue when evaluating the surrogate model outside of its initial
training range during the online stage. This 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 simulation was reduced by up to 75%
while maintaining an error of less than 10% on relevant quantities of interest.
