“DDPS | Intrusive model order reduction using neural network approximants”

DDPS Talk date: July 12th, 2024
Speaker: Francesco Romor (Weierstrass Institute, www.wias-berli...)
Description: A slowly decaying Kolmogorov n-width of the solution manifold for a parametric partial differential equation hinders the development of efficient linear projection-based reduced-order models. This is due to the high dimensionality of the reduced space required to accurately approximate the solution manifold. To address this issue, neural networks, through various architectures, have been utilized to design accurate nonlinear regressions of solution manifolds. However, most implementations are non-intrusive black-box surrogate models, and only some perform dimensional reduction from the number of degrees of freedom of the discretized parametric models to a latent dimension. We introduce a novel intrusive and interpretable methodology for reduced-order modeling that uses neural networks as solution manifold approximants while retaining the underlying physical and numerical models during the predictive/online stage. Specifically, we focus on autoencoders to further compress the dimensionality of linear approximations of solution manifolds, ultimately achieving nonlinear dimension reduction. After obtaining an accurate nonlinear approximation, we seek solutions on the latent manifold using the residual-based nonlinear least-squares Petrov-Galerkin method, suitably hyper-reduced to be independent of the number of degrees of freedom. We develop new adaptive hyper-reduction strategies and demonstrate the feasibility of employing also local nonlinear approximants. We validate our methodology on two nonlinear, time-dependent parametric benchmarks: a supersonic flow past a NACA airfoil with varying Mach number and an incompressible turbulent flow around the Ahmed body with changing slant angle.
DDPS webinar: www.librom.net...
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IM release number is: LLNL-VIDEO-866743