Localized Model Order Reduction for Parameter Optimization with Multiscale PDE Constraints

Explore localized model order reduction techniques for parameter optimization with multiscale PDE constraints in this 56-minute lecture by Mario Ohlberger from the Hausdorff Center for Mathematics. Delve into the reduced basis method for parameterized partial differential equations, examining its advantages in enabling high-fidelity real-time simulations and reducing computational costs in many-query applications. Investigate the challenges of large-scale and multiscale systems, focusing on localized training and on-the-fly enrichment strategies for PDE constrained optimization. Learn about the reduced basis - trust region framework, rigorous certification, and convergence concepts. Examine numerical experiments demonstrating the efficiency of proposed approaches in overcoming limitations of classical offline/online splitting methods.