RONAALP: Reduced-Order Nonlinear Approximation with Active Learning Procedure

arXiv (Cornell University)

Abstract

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.

Authors 4

1. Clément Scherding

   Sorbonne Université · Institut Jean Le Rond d'Alembert

   Affiliation as printed

   Institut Jean le Rond d'Alembert, Sorbonne University

2. Denis Sipp

   Office National d'Études et de Recherches Aérospatiales

   Affiliation as printed

   DAAA, Onera

3. Peter J. Schmid

   King Abdullah University of Science and Technology

   Affiliation as printed

   Department of Mechanical Engineering, KAUST

4. Taraneh Sayadi Aachen Institute for Combustion Technology

   Sorbonne Université · Institut Jean Le Rond d'Alembert · RWTH Aachen University

   Affiliation as printed

   Institut Jean le Rond d'Alembert, Sorbonne University

   Institute for Combustion Technology, Aachen University