Discovery and Model Reduction of Hamiltonian Systems
Peter Benner
Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg
One often encountered computational issue in studying nuclear fusion reactors is the simulation of the behavior of confined plasmas in a controlled magnetic field. Numerical modeling requires the solution of the Vlasov equation, potentially coupled to other partial differential equations. After spatial discretization, this leads to high-dimensional Hamiltonian systems. Fast simulation under varying conditions requires learning a compact, reduced-order model that is fast to simulate and faithfully reproduces the kinetics of the full-order model. We discuss several approaches to learn Hamiltonian systems from data. Model reduction can be achieved using variational autoencoders. We show how the underlying Hamiltonian structure, resulting in a symplectic flow field, can be preserved using symplectic convolutional neural networks. This talk will discuss joint research with Thomas Bendokat, Konrad Janik, Pawan K. Goyal, Igor Pontes Duff, and Süleyman Yildiz.