Symplectic Neural Operators for Learning Infinite Dimensional Hamiltonian Systems
The paper introduces Symplectic Neural Operators (SNOs) designed for modeling infinite-dimensional Hamiltonian systems. These operators aim to preserve the symplectic structure inherent in Hamiltonian partial differential equations (PDEs). The authors provide theoretical and numerical evidence supporting the effectiveness of SNOs in maintaining stability and improving energy behavior compared to traditional neural operators.
- ▪Symplectic Neural Operators are introduced to address challenges in modeling infinite-dimensional Hamiltonian systems.
- ▪The architecture is designed to preserve the symplectic structure intrinsic to Hamiltonian PDEs.
- ▪Theoretical results demonstrate long-term stability and improved energy behavior of SNOs over non-structure-preserving neural operators.
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Mathematics > Dynamical Systems arXiv:2605.15881 (math) [Submitted on 15 May 2026] Title:Symplectic Neural Operators for Learning Infinite Dimensional Hamiltonian Systems Authors:Yeang Makara, Yusuke Tanaka, Takashi Matsubara, Takaharu Yaguchi View a PDF of the paper titled Symplectic Neural Operators for Learning Infinite Dimensional Hamiltonian Systems, by Yeang Makara and 3 other authors View PDF HTML (experimental) Abstract: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.
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