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.

翻译：许多工程应用依赖于评估昂贵且非线性的高维函数。本文提出RONAALP算法（基于主动学习过程的降阶非线性逼近方法），旨在随应用进程在线增量学习目标函数的快速精确降阶替代模型。首先，非线性自编码器、社区聚类与径向基函数网络的结合，允许利用有限训练数据学习高效紧凑的替代模型。其次，主动学习过程可克服在线阶段在初始训练范围外评估替代模型时的外推问题。由此得到的高维函数降阶模型兼具泛化性、快速性与精确性。该方法在三个化学非平衡高超声速流动的直接数值模拟中进行了验证。此类流动的精确模拟依赖于详细热化学气体模型，而这会显著增加计算成本。使用RONAALP在线学习降阶热力学模型替代后，模拟成本最高降低75%，同时相关感兴趣量的误差控制在10%以内。