We are happy to announce that our submission "Symplectic Model Reduction of Hamiltonian Systems on Nonlinear Manifolds and Approximation with Weakly Symplectic Autoencoder" was accepted and published in the SIAM Journal on Scientific Computing. The work was a collaboration with Silke Glas from the University of Twente. In our article, we introduce structure-preserving MOR for Hamiltonian systems with symplectic nonlinear maps. Moreover, we suggest a weakly symplectic autoencoder as a symplectic nonlinear map based on artifical neural networks. In a numerical experiment, we consider a linear wave equation with initial data which is hard to reduce for classical MOR and demonstrate the superiority in accuracy with the newly introduced method.
Symplectic Model Reduction of Hamiltonian Systems on Nonlinear Manifolds and Approximation with Weakly Symplectic Autoencoder