Institute of Mathematics

Talk

Modul:   MAT870  Zurich Colloquium in Applied and Computational Mathematics

Structure-​preserving dynamical reduced basis methods for parametrized Hamiltonian systems

Prof. Dr. Cecilia Pagliantini talk

Date: 11.11.20  Time: 16.15 - 17.45  Room: Online ZHACM

In real-​time and many-​query simulations of parametrized differential equations, computational methods need to face high computational costs to provide sufficiently accurate numerical solutions. To address this issue, model order reduction techniques aim at constructing low-​complexity high-​fidelity surrogate models that allow rapid and accurate solutions under parameter variation. In this talk, we will consider reduced basis methods (RBM) for the model order reduction of parametrized Hamiltonian dynamical systems describing nondissipative phenomena. The development of RBM for Hamiltonian systems is challenged by two main factors: (i) failing to preserve the geometric structure encoding the physical properties of the dynamics might lead to instabilities and unphysical behaviors; (ii) the local low-​rank nature of nondissipative dynamics demands large reduced spaces to achieve sufficiently accurate approximations. We will discuss how to address these aspects via nonlinear reduced basis methods based on the characterization of the reduced dynamics on a phase space that evolves in time and is endowed with the geometric structure of the full model.