Feb. 9, 2024, 5:44 a.m. | S\"uleyman Yildiz Pawan Goyal Thomas Bendokat Peter Benner

cs.LG updates on arXiv.org arxiv.org

We present a framework for learning Hamiltonian systems using data. This work is based on a lifting hypothesis, which posits that nonlinear Hamiltonian systems can be written as nonlinear systems with cubic Hamiltonians. By leveraging this, we obtain quadratic dynamics that are Hamiltonian in a transformed coordinate system. To that end, for given generalized position and momentum data, we propose a methodology to learn quadratic dynamical systems, enforcing the Hamiltonian structure in combination with a weakly-enforced symplectic auto-encoder. The obtained …

cs.lg data data-driven dynamics framework hypothesis identification systems work

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