mlsanityData to 13 Oct 2026

A Riemannian Framework for Learning Reduced-order Lagrangian Dynamics

arXiv 2410.18868 ↗First posted 24 Oct 2024cs.LGcited by 7

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Abstract (arXiv)

By incorporating physical consistency as inductive bias, deep neural networks display increased generalization capabilities and data efficiency in learning nonlinear dynamic models. However, the complexity of these models generally increases with the system dimensionality, requiring larger datasets, more complex deep networks, and significant computational effort. We propose a novel geometric network architecture to learn physically-consistent reduced-order dynamic parameters that accurately describe the original high-dimensional system behavior. This is achieved by building on recent advances in model-order reduction and by adopting a Riemannian perspective to jointly learn a non-linear structure-preserving latent space and the associated low-dimensional dynamics. Our approach enables accurate long-term predictions of the high-dimensional dynamics of rigid and deformable systems with increased data efficiency by inferring interpretable and physically-plausible reduced Lagrangian models.

Key facts. Cited by 7 papers in the map (data through 13 Oct 2026). Builds on 25 of its 41 references that are in the map. First posted on arXiv 24 Oct 2024.

Builds on

25 of 41 references.

References · 25

  1. 2018Neural Ordinary Differential Equationscited by 3,750
  2. 2019Hamiltonian Neural Networkscited by 705
  3. 2018Hyperbolic Neural Networkscited by 396
  4. 2020Lagrangian Neural Networkscited by 392
  5. 2019Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learningcited by 207
  6. 2018Riemannian Adaptive Optimization Methodscited by 191
  7. 2016A Riemannian Network for SPD Matrix Learningcited by 162
  8. 2020Geoopt: Riemannian Optimization in PyTorchcited by 111
  9. 2020Simplifying Hamiltonian and Lagrangian Neural Networks via Explicit Constraintscited by 103
  10. 2020Unsupervised Learning of Lagrangian Dynamics from Images for Prediction and Controlcited by 38
  11. 2021Hamiltonian-based Neural ODE Networks on the SE(3) Manifold For Dynamics Learning and Controlcited by 37
  12. 2021Extending Lagrangian and Hamiltonian Neural Networks with Differentiable Contact Modelscited by 33
13 more
  1. 2022Quadratic Approximation Manifold for Mitigating the Kolmogorov Barrier in Nonlinear Projection-Based Model Order Reductioncited by 29
  2. 2021Which priors matter? Benchmarking models for learning latent dynamicscited by 26
  3. 2021Vector-valued Distance and Gyrocalculus on the Space of Symmetric Positive Definite Matricescited by 22
  4. 2021Combining Physics and Deep Learning to learn Continuous-Time Dynamics Modelscited by 20
  5. 2023Learning Nonlinear Projections for Reduced-Order Modeling of Dynamical Systems using Constrained Autoencoderscited by 16
  6. 2024Lagrangian operator inference enhanced with structure-preserving machine learning for nonintrusive model reduction of mechanical systemscited by 16
  7. 2022Learning Hamiltonians of constrained mechanical systemscited by 14
  8. 2023Symplectic model reduction of Hamiltonian systems using data-driven quadratic manifoldscited by 13
  9. 2024Matrix Manifold Neural Networks++cited by 13
  10. 2014Preserving Lagrangian structure in nonlinear model reduction with application to structural dynamicscited by 10
  11. 2021Learning Contact Dynamics using Physically Structured Neural Networkscited by 10
  12. 2023Neural Autoencoder-Based Structure-Preserving Model Order Reduction and Control Design for High-Dimensional Physical Systemscited by 7
  13. 2022Physically Consistent Learning of Conservative Lagrangian Systems with Gaussian Processescited by 5

Built on by

Cited by year (2026 to 13 Oct)

Citing papers per year: 2025: 4; 2026: 3.

7 papers.

  1. 2025Physics-Informed Latent Neural Operator for Real-time Predictions of time-dependent parametric PDEscited by 9
  2. 2025GeoHNNs: Geometric Hamiltonian Neural Networkscited by 3
  3. 2025Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approachcited by 2
  4. 2025Nonlinear Model Order Reduction of Dynamical Systems in Process Engineering: Review and Comparisoncited by 0
  5. 2026Context-dependent manifold learning: A neuromodulated constrained autoencoder approachcited by 0
  6. 2026LaGSplat: Inferring Physics-Governed Interactive Simulation from Monocular Video Using Latent Lagrangian Gaussian Splattingcited by 0
  7. 2026Partially Linear Autoencoders for Manifold Learning and Dimensionality Reductioncited by 0