mlsanityData to 14 Oct 2026

Structure-preserving Method for Reconstructing Unknown Hamiltonian Systems from Trajectory Data

arXiv 1905.10396 ↗First posted 24 May 2019math.NA cs.LG cs.NAcited by 18

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Abstract (arXiv)

We present a numerical approach for approximating unknown Hamiltonian systems using observation data. A distinct feature of the proposed method is that it is structure-preserving, in the sense that it enforces conservation of the reconstructed Hamiltonian. This is achieved by directly approximating the underlying unknown Hamiltonian, rather than the right-hand-side of the governing equations. We present the technical details of the proposed algorithm and its error estimate in a special case, along with a practical de-noising procedure to cope with noisy data. A set of numerical examples are then presented to demonstrate the structure-preserving property and effectiveness of the algorithm.

Key facts. Cited by 18 papers in the map (data through 14 Oct 2026). First posted on arXiv 24 May 2019.

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 4; 2022: 4; 2023: 3; 2024: 2; 2025: 3; 2026: 2.

18 papers.

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  1. 2021Data-driven Prediction of General Hamiltonian Dynamics via Learning Exactly-Symplectic Mapscited by 41
  2. 2021Adaptive deep density approximation for Fokker-Planck equationscited by 28
  3. 2021Deep Neural Network Modeling of Unknown Partial Differential Equations in Nodal Spacecited by 25
  4. 2023Deep-OSG: Deep Learning of Operators in Semigroupcited by 11
  5. 2021Learning Large-Time-Step Molecular Dynamics with Graph Neural Networkscited by 9
  6. 2025DUE: A Deep Learning Framework and Library for Modeling Unknown Equationscited by 8
  7. 2023Implementation and (Inverse Modified) Error Analysis for implicitly-templated ODE-netscited by 6
  8. 2022Modeling unknown dynamical systems with hidden parameterscited by 4
  9. 2022Learning Trajectories of Hamiltonian Systems with Neural Networkscited by 4
  10. 2022Bayesian Identification of Nonseparable Hamiltonian Systems Using Stochastic Dynamic Modelscited by 3
  11. 2022VPNets: Volume-preserving neural networks for learning source-free dynamicscited by 2
  12. 2024Bayesian identification of nonseparable Hamiltonians with multiplicative noise using deep learning and reduced-order modelingcited by 2
6 more
  1. 2026Hypothesis-driven construction of mesoscopic dynamicscited by 2
  2. 2024Aligning AI-driven discovery with human intuitioncited by 1
  3. 2025H-FEX: A Symbolic Learning Method for Hamiltonian Systemscited by 1
  4. 2025Learning Stochastic Hamiltonian Systems via Stochastic Generating Function Neural Networkcited by 1
  5. 2026CSympNet-ID: conformal-symplectic map learning for linearly damped Hamiltonian systemscited by 1
  6. 2023Critical Sampling for Robust Evolution Operator Learning of Unknown Dynamical Systemscited by 0