Minisymposium Presentation

In this talk we perform structure-preserving reduced order modeling for the semi-discretized Hamiltonian PDEs. Reduced order modeling can alleviate the cost involved in applications such as optimization, uncertainty quantification and inverse problems, that require the repeated solution of large-dimensional physical systems. For this task we can use neural networks among other techniques.We start by giving a short overview of methods for performing reduced order modeling and how to make them structure-preserving. A focus will be put on symplectic autoencoders. These are neural networks that respect the symplectic structure of the underlying differential equation. We will show the advantages of both structure preservation and neural networks, compared to other techniques, when performing reduced order modeling for Hamiltonian systems and discuss future challenges ahead for dealing with real-world magnetic fusion plasmas.