Symplectic Neural Operators for Learning Infinite Dimensional Hamiltonian Systems
The modeling and simulation of infinite-dimensional Hamiltonian systems are central problems in mathematical physics and engineering, however they pose significant computational and structural challenges for standard data-driven architectures. In this work, we introduce the Symplectic Neural Operator, a neural operator architecture designed to preserve the symplectic structure intrinsic to Hamiltonian PDEs. We provide a theoretical characterization of their symplecticity and establish a rigorous long-term stability result based on the combination of symplectic structure preservation and learning accuracy. Numerical experiments on canonical Hamiltonian PDEs corroborate this theoretical res...
| Authors | Yeang Makara, Yusuke Tanaka, Takashi Matsubara et al. |
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| Primary category | math.DS |
| Published | 15 May 2026 |
| Last updated at source | 15 May 2026 |
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