mlsanityData to 14 Oct 2026

Symplectic Neural Operators for Learning Infinite Dimensional Hamiltonian Systems

arXiv 2605.15881 ↗First posted 15 May 2026math.DS cs.AI physics.comp-phcited by 3

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Abstract (arXiv)

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 result and show that SNOs exhibit improved energy behavior compared with non-structure-preserving neural operators.

Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Builds on 6 of its 20 references that are in the map. First posted on arXiv 15 May 2026.

Builds on

6 of 20 references.

References · 6

  1. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
  2. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 2,018
  3. 2021Physics-Informed Neural Operator for Learning Partial Differential Equationscited by 527
  4. 2020Lagrangian Neural Networkscited by 398
  5. 2020Multipole Graph Neural Operator for Parametric Partial Differential Equationscited by 349
  6. 2023Convolutional Neural Operators for robust and accurate learning of PDEscited by 214

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 3.

3 papers.

  1. 2026Cost-Accuracy Trade-offs: Neural Operator vs Classical Numerical Solvercited by 0
  2. 2026Elucidating the Conformal Structure of the Brinkman Penalisation Method for Geometry-Adapted, Structure-Preserving Operator Learning of Hamiltonian PDEscited by 0
  3. 2026The limits of exactness: On the failure of automatic differentiation in physics-informed machine learningcited by 0