Seminar by Cecilia Pagliantini

Speaker

Cecilia Pagliantini (Università di Pisa)

Title

Structure-preserving nonlinear model order reduction of parametric Hamiltonian systems

Date

• November 14, 2023 16:00 CET+0100 (Europe/Rome)

• November 14, 2023 10:00 EST-0500 (US/Eastern)

• November 14, 2023 09:00 CST-0600 (US/Central)

• November 14, 2023 07:00 PST-0800 (US/Pacific)

Abstract

Hamiltonian systems describe conservative phenomena ranging from transport problems to conservation laws in fluid dynamics and plasma physics. The development of reduced order models for Hamiltonian systems is challenged by several factors: (i) failing to preserve the geometric structure encoding the physical properties of the dynamics might lead to instabilities and unphysical behaviors of the resulting approximate solutions; (ii) the slowly decaying Kolmogorov n-width of transport-dominated and non-dissipative phenomena demands large reduced spaces to achieve sufficiently accurate approximations; and (iii) nonlinear operators require hyper-reduction techniques that preserve the gradient structure of the flow velocity. We will discuss how to address these aspects via structure-preserving nonlinear model order reduction. The gist of the proposed method is to adapt in time an approximate low-dimensional phase space endowed with the geometric structure of the full model and to ensure that the hyper-reduced flow retains the physical properties of the original model.

Recording

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