mlsanityData to 7 Oct 2026

Canonical and Noncanonical Hamiltonian Operator Inference

arXiv 2304.06262 ↗First posted 13 Apr 2023cs.LG math.DScited by 15

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Abstract (arXiv)

A method for the nonintrusive and structure-preserving model reduction of canonical and noncanonical Hamiltonian systems is presented. Based on the idea of operator inference, this technique is provably convergent and reduces to a straightforward linear solve given snapshot data and gray-box knowledge of the system Hamiltonian. Examples involving several hyperbolic partial differential equations show that the proposed method yields reduced models which, in addition to being accurate and stable with respect to the addition of basis modes, preserve conserved quantities well outside the range of their training data.

Key facts. Cited by 15 papers in the map (data through 7 Oct 2026). Builds on 13 of its 90 references that are in the map. First posted on arXiv 13 Apr 2023.

Builds on

13 of 90 references.

References · 13

  1. 2019Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systemscited by 96
  2. 2020A fast and accurate physics-informed neural network reduced order model with shallow masked autoencodercited by 80
  3. 2020Data-driven reduced-order models via regularized operator inference for a single-injector combustion processcited by 42
  4. 2020Operator inference for non-intrusive model reduction of systems with non-polynomial nonlinear termscited by 32
  5. 2022Quadratic Approximation Manifold for Mitigating the Kolmogorov Barrier in Nonlinear Projection-Based Model Order Reductioncited by 29
  6. 2021A Comparison of Neural Network Architectures for Data-Driven Reduced-Order Modelingcited by 22
  7. 2019Learning physics-based reduced-order models for a single-injector combustion processcited by 20
  8. 2019Sampling low-dimensional Markovian dynamics for pre-asymptotically recovering reduced models from data with operator inferencecited by 20
  9. 2022Bayesian operator inference for data-driven reduced-order modelingcited by 19
  10. 2018Nonlinear Model Order Reduction via Lifting Transformations and Proper Orthogonal Decompositioncited by 14
  11. 2014Preserving Lagrangian structure in nonlinear model reduction with application to structural dynamicscited by 10
  12. 2019Balanced Truncation Model Reduction for Lifted Nonlinear Systemscited by 5
1 more
  1. 2022Neural-Network-Augmented Projection-Based Model Order Reduction for Mitigating the Kolmogorov Barrier to Reducibility of CFD Modelscited by 5

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 5; 2024: 1; 2025: 7; 2026: 2.

15 papers.

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  1. 2023Symplectic model reduction of Hamiltonian systems using data-driven quadratic manifoldscited by 13
  2. 2023Guaranteed Stable Quadratic Models and their applications in SINDy and Operator Inferencecited by 10
  3. 2025Thermodynamically Consistent Latent Dynamics Identification for Parametric Systemscited by 8
  4. 2023Data-Driven Identification of Quadratic Representations for Nonlinear Hamiltonian Systems using Weakly Symplectic Liftingscited by 6
  5. 2024Energy-Preserving Reduced Operator Inference for Efficient Design and Controlcited by 4
  6. 2023Deep Learning for Structure-Preserving Universal Stable Koopman-Inspired Embeddings for Nonlinear Canonical Hamiltonian Dynamicscited by 3
  7. 2023Nonlinear embeddings for conserving Hamiltonians and other quantities with Neural Galerkin schemescited by 3
  8. 2025Nested Operator Inference for Adaptive Data-Driven Learning of Reduced-order Modelscited by 3
  9. 2025Physically consistent predictive reduced-order modeling by enhancing Operator Inference with state constraintscited by 2
  10. 2025Nonlinear energy-preserving model reduction with lifting transformations that quadratize the energycited by 2
  11. 2025Operator Inference Aware Quadratic Manifolds with Isotropic Reduced Coordinates for Nonintrusive Model Reductioncited by 2
  12. 2026Streaming Operator Inference for Model Reduction of Large-Scale Dynamical Systemscited by 2
3 more
  1. 2026NN-OpInf: an operator inference approach using structure-preserving composable neural networkscited by 1
  2. 2025Nonlinear Model Order Reduction of Dynamical Systems in Process Engineering: Review and Comparisoncited by 0
  3. 2025Structure-preserving Lift & Learn: Scientific machine learning for nonlinear conservative partial differential equationscited by 0