|Abstract:|| Reduced basis (RB) methods represent a reliable and efficient approach for the numerical approximation of problems involving the repeated solution of differential equations arising from engineering and applied sciences. Noteworthy examples include partial differential equations (PDEs) depending on several parameters, PDE-constrained optimization,
data assimilation and uncertainty quantification problems. When dealing with more complex nonaffine and/or nonlinear problems, several challenges have to be faced to ensure accuracy and computational efficiency. These involve, among others, the need of (i) generating the reduced problem in non-intrusive and purely algebraic way; (ii) estimating the reduction errors or providing effective error surrogates; (iii) approximating manifolds of large intrinsic dimension with low-dimensional subspaces through possibly nonlinear or localized model order reduction algorithms.
In this talk I will show how to combine some recent reduction and hyper-reduction techniques to solve a variety of
computationally-intensive problems ranging, e.g., from fluid dynamics on domains with varying shape to cardiac electrophysiology and parameter estimation in a Bayesian setting.