Learning symplectic model reduction based on a approximation theorem of symplectic embeddings

ArXi:2606.04623v1 Announce Type: new High-dimensional Hamiltonian systems play a central role in many scientific and engineering disciplines, with dynamics evolving on symplectic manifolds. Although deep learning provides powerful tools for constructing low-dimensional surrogates from data, the intrinsic symplectic structure is easily destroyed during model reduction. As a result, a standard autoencoder may produce latent coordinates that do not a Hamiltonian flow, leading to unstable long-time prediction.