mlsanityData to 14 Oct 2026

Deep Learning for Structure-Preserving Universal Stable Koopman-Inspired Embeddings for Nonlinear Canonical Hamiltonian Dynamics

arXiv 2308.13835 ↗First posted 26 Aug 2023cs.LG cs.AI math.DScited by 3

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Abstract (arXiv)

Discovering a suitable coordinate transformation for nonlinear systems enables the construction of simpler models, facilitating prediction, control, and optimization for complex nonlinear systems. To that end, Koopman operator theory offers a framework for global linearization for nonlinear systems, thereby allowing the usage of linear tools for design studies. In this work, we focus on the identification of global linearized embeddings for canonical nonlinear Hamiltonian systems through a symplectic transformation. While this task is often challenging, we leverage the power of deep learning to discover the desired embeddings. Furthermore, to overcome the shortcomings of Koopman operators for systems with continuous spectra, we apply the lifting principle and learn global cubicized embeddings. Additionally, a key emphasis is paid to enforce the bounded stability for the dynamics of the discovered embeddings. We demonstrate the capabilities of deep learning in acquiring compact symplectic coordinate transformation and the corresponding simple dynamical models, fostering data-driven learning of nonlinear canonical Hamiltonian systems, even those with continuous spectra.

Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Builds on 20 of its 69 references that are in the map. First posted on arXiv 26 Aug 2023.

Builds on

20 of 69 references.

References · 20

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8 more
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Cited by year

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

3 papers.

  1. 2025One-Step Offline Distillation of Diffusion-based Models via Koopman Modelingcited by 9
  2. 2025Symplectic convolutional neural networkscited by 1
  3. 2024Structure-preserving learning for multi-symplectic PDEscited by 0