mlsanityData to 14 Oct 2026

Data-Driven Identification of Quadratic Representations for Nonlinear Hamiltonian Systems using Weakly Symplectic Liftings

arXiv 2308.01084 ↗First posted 2 Aug 2023cs.LGcited by 6

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Abstract (arXiv)

We present a framework for learning Hamiltonian systems using data. This work is based on a lifting hypothesis, which posits that nonlinear Hamiltonian systems can be written as nonlinear systems with cubic Hamiltonians. By leveraging this, we obtain quadratic dynamics that are Hamiltonian in a transformed coordinate system. To that end, for given generalized position and momentum data, we propose a methodology to learn quadratic dynamical systems, enforcing the Hamiltonian structure in combination with a weakly-enforced symplectic auto-encoder. The obtained Hamiltonian structure exhibits long-term stability of the system, while the cubic Hamiltonian function provides relatively low model complexity. For low-dimensional data, we determine a higher-dimensional transformed coordinate system, whereas for high-dimensional data, we find a lower-dimensional coordinate system with the desired properties. We demonstrate the proposed methodology by means of both low-dimensional and high-dimensional nonlinear Hamiltonian systems.

Key facts. Cited by 6 papers in the map (data through 14 Oct 2026). Builds on 17 of its 50 references that are in the map. First posted on arXiv 2 Aug 2023.

Builds on

17 of 50 references.

References · 17

  1. 2019Hamiltonian Neural Networkscited by 712
  2. 2017Deep learning for universal linear embeddings of nonlinear dynamicscited by 494
  3. 2018Data-Driven Forecasting of High-Dimensional Chaotic Systems with Long Short-Term Memory Networkscited by 155
  4. 2019Symplectic Recurrent Neural Networkscited by 150
  5. 2018Multivariate LSTM-FCNs for Time Series Classificationcited by 120
  6. 2020Simplifying Hamiltonian and Lagrangian Neural Networks via Explicit Constraintscited by 105
  7. 2019Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systemscited by 96
  8. 2022GREAD: Graph Neural Reaction-Diffusion Networkscited by 54
  9. 2016Inferring solutions of differential equations using noisy multi-fidelity datacited by 38
  10. 2020Hamiltonian neural networks for solving equations of motioncited by 33
  11. 2023Reversible and irreversible bracket-based dynamics for deep graph neural networkscited by 26
  12. 2020Symplectic Neural Networks in Taylor Series Form for Hamiltonian Systemscited by 24
5 more
  1. 2020Forecasting Hamiltonian dynamics without canonical coordinatescited by 17
  2. 2023Canonical and Noncanonical Hamiltonian Operator Inferencecited by 15
  3. 2023Symplectic model reduction of Hamiltonian systems using data-driven quadratic manifoldscited by 13
  4. 2022Generalized Quadratic Embeddings for Nonlinear Dynamics using Deep Learningcited by 9
  5. 2021Level set learning with pseudo-reversible neural networks for nonlinear dimension reduction in function approximationcited by 4

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Cited by year

Citing papers per year: 2023: 1; 2024: 2; 2025: 3.

6 papers.

  1. 2023Deep Learning for Structure-Preserving Universal Stable Koopman-Inspired Embeddings for Nonlinear Canonical Hamiltonian Dynamicscited by 3
  2. 2024Data-driven identification of latent port-Hamiltonian systemscited by 3
  3. 2025Symplectic convolutional neural networkscited by 1
  4. 2025Time-adaptive SympNets for separable Hamiltonian systemscited by 1
  5. 2025Time-adaptive H'enonNets for separable Hamiltonian systemscited by 1
  6. 2024Structure-preserving learning for multi-symplectic PDEscited by 0