Intrusive Model Order Reduction Using Neural Network Approximants

Explore an innovative approach to intrusive model order reduction using neural network approximants in this hour-long talk by Francesco Romor from the Weierstrass Institute. Delve into the challenges of developing efficient linear projection-based reduced-order models for parametric partial differential equations with slowly decaying Kolmogorov n-width. Learn how neural networks, particularly autoencoders, are employed to achieve nonlinear dimension reduction and compress the dimensionality of linear approximations of solution manifolds. Discover a novel intrusive and interpretable methodology for reduced-order modeling that retains underlying physical and numerical models during the predictive stage. Examine the use of residual-based nonlinear least-squares Petrov-Galerkin method and new adaptive hyper-reduction strategies. Gain insights into the validation of this methodology through 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.