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

Excerpt

arXiv:2606.04623v2 Announce Type: replace Abstract: High-dimensional Hamiltonian systems play a central role in many scientific and engineering disciplines, with dynamics that evolve on symplectic manifolds. Although deep learning provides powerful tools for constructing its 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 support a Hamiltonian flow,