RONAALP: Reduced-Order Nonlinear Approximation with Active Learning Procedure

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.

Data-driven framework for input/output lookup tables reduction -- with application to hypersonic flows in chemical non-equilibrium

In this paper, we present a novel model-agnostic machine learning technique to extract a reduced thermochemical model for reacting hypersonic flows simulation. A first simulation gathers all relevant thermodynamic states and the corresponding gas properties via a given model. The states are embedded in a low-dimensional space and clustered to identify regions with different levels of thermochemical (non)-equilibrium. Then, a surrogate surface from the reduced cluster-space to the output space is generated using radial-basis-function networks. The method is validated and benchmarked on a simulation of a hypersonic flat-plate boundary layer with finite-rate chemistry. The gas properties of the reactive air mixture are initially modeled using the open-source Mutation++ library. Substituting Mutation++ with the light-weight, machine-learned alternative improves the performance of the solver by 50% while maintaining overall accuracy.