Reduced-order modeling of Hamiltonian dynamics based on symplectic neural networks
This work addresses the need for efficient and stable reduced-order models for complex dynamical systems in scientific and engineering fields, representing an incremental improvement by integrating symplectic neural networks into a unified architecture.
The paper tackled the problem of high-dimensional Hamiltonian systems by introducing a data-driven symplectic reduced-order modeling framework that unifies latent-space discovery and dynamics learning, resulting in accurate trajectory reconstruction, robust predictive performance, and exact Hamiltonian preservation as validated in numerical experiments.
We introduce a novel data-driven symplectic induced-order modeling (ROM) framework for high-dimensional Hamiltonian systems that unifies latent-space discovery and dynamics learning within a single, end-to-end neural architecture. The encoder-decoder is built from Henon neural networks (HenonNets) and may be augmented with linear SGS-reflector layers. This yields an exact symplectic map between full and latent phase spaces. Latent dynamics are advanced by a symplectic flow map implemented as a HenonNet. This unified neural architecture ensures exact preservation of the underlying symplectic structure at the reduced-order level, significantly enhancing the fidelity and long-term stability of the resulting ROM. We validate our method through comprehensive numerical experiments on canonical Hamiltonian systems. The results demonstrate the method's capability for accurate trajectory reconstruction, robust predictive performance beyond the training horizon, and accurate Hamiltonian preservation. These promising outcomes underscore the effectiveness and potential applicability of our symplectic ROM framework for complex dynamical systems across a broad range of scientific and engineering disciplines.