Symplectic Neural Operators for Hamiltonian PDEs
A new neural operator architecture, the Symplectic Neural Operator (SNO), preserves the symplectic structure of infinite-dimensional Hamiltonian systems. The method is designed for modeling Hamiltonian partial differential equations (PDEs) and is shown to improve long-term energy stability compared to non-structure-preserving neural operators. Theoretical results establish symplecticity and stability, corroborated by numerical experiments on canonical Hamiltonian PDEs. The work addresses computational challenges in mathematical physics and engineering.
Key facts
- Symplectic Neural Operator (SNO) introduced for infinite-dimensional Hamiltonian systems.
- Preserves symplectic structure intrinsic to Hamiltonian PDEs.
- Theoretical characterization of symplecticity and long-term stability.
- Numerical experiments on canonical Hamiltonian PDEs confirm improved energy behavior.
- Compared with non-structure-preserving neural operators.
- Addresses computational and structural challenges in data-driven modeling.
- Relevant to mathematical physics and engineering.
- Submitted to arXiv on an unspecified date.
Entities
Institutions
- arXiv