Inspired by our previous work on mitigating the Kolmogorov barrier using a quadratic approximation manifold, we propose in this paper a computationally tractable approach for combining a projection-based reduced-order model (PROM) and an artificial neural network (ANN) for mitigating the Kolmogorov barrier to reducibility of convection-dominated flow problems. The main objective the PROM-ANN concept that we propose is to reduce the dimensionality of the online approximation of the solution beyond what is possible using affine and quadratic approximation manifolds. In contrast to previous approaches for constructing arbitrarily nonlinear manifold approximations for nonlinear model reduction that exploited one form or another of ANN, the training of the PROM-ANN we propose in this paper does not involve data whose dimension scales with that of the high-dimensional model; and this PROM-ANN is hyperreducible using any well-established hyperreduction method. Hence, unlike many other ANN-based approaches, the PROM-ANN concept we propose in this paper is practical for large-scale and industry-relevant CFD problems. Its potential is demonstrated here for a parametric, shock-dominated, benchmark problem.
翻译:由于我们先前利用四面形近似模型减轻科尔莫戈洛夫屏障的工作,我们在本文件中提出一种可计算化的办法来合并基于投影的减序模型(PROM)和人工神经网络(ANN),以减少科尔莫戈洛夫屏障,从而减少对流主导流动问题的影响。我们提议的PROM-ANN概念的主要目标是减少解决办法在线近似的维度,使其超出使用断裂和四面形近似模型的可能范围。与以前用来为非线性模型的削减建立任意的非线性非线性多元近似的方法相比,我们在本文件中提议的对PROM-ANN的培训并不涉及其尺寸与高维形模型相比的数据;而这个PROM-ANNN概念使用任何既定的超降率方法都非常容易减轻。因此,与许多其他基于ANNE的办法不同,我们在本文件中提议的PROM-ANNN概念对于大规模和工业相关问题的CFD问题来说是实用的。我们在这里提出的PROM-ANNNN概念,它的潜力是用来测定冲击问题的基准。