mlsanityData to 7 Oct 2026

Learning POD of Complex Dynamics Using Heavy-ball Neural ODEs

arXiv 2202.12373 ↗First posted 24 Feb 2022cs.LG cs.NA math.NAcited by 2

Not on the map. Why?

Abstract (arXiv)

Proper orthogonal decomposition (POD) allows reduced-order modeling of complex dynamical systems at a substantial level, while maintaining a high degree of accuracy in modeling the underlying dynamical systems. Advances in machine learning algorithms enable learning POD-based dynamics from data and making accurate and fast predictions of dynamical systems. In this paper, we leverage the recently proposed heavy-ball neural ODEs (HBNODEs) [Xia et al. NeurIPS, 2021] for learning data-driven reduced-order models (ROMs) in the POD context, in particular, for learning dynamics of time-varying coefficients generated by the POD analysis on training snapshots generated from solving full order models. HBNODE enjoys several practical advantages for learning POD-based ROMs with theoretical guarantees, including 1) HBNODE can learn long-term dependencies effectively from sequential observations and 2) HBNODE is computationally efficient in both training and testing. We compare HBNODE with other popular ROMs on several complex dynamical systems, including the von K'arm'an Street flow, the Kurganov-Petrova-Popov equation, and the one-dimensional Euler equations for fluids modeling.

Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 19 of its 65 references that are in the map. First posted on arXiv 24 Feb 2022.

Builds on

19 of 65 references.

References · 19

  1. 2014Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translationcited by 4,016
  2. 2018Neural Ordinary Differential Equationscited by 3,733
  3. 2018Neural Tangent Kernel: Convergence and Generalization in Neural Networkscited by 2,597
  4. 2016Identity Mappings in Deep Residual Networkscited by 1,960
  5. 2019Augmented Neural ODEscited by 396
  6. 2020Dissecting Neural ODEscited by 150
  7. 2020Learning Long-Term Dependencies in Irregularly-Sampled Time Seriescited by 82
  8. 2020On Second Order Behaviour in Augmented Neural ODEscited by 68
  9. 2021Heavy Ball Neural Ordinary Differential Equationscited by 42
  10. 2020Scheduled Restart Momentum for Accelerated Stochastic Gradient Descentcited by 24
  11. 2017DR-RNN: A deep residual recurrent neural network for model reductioncited by 20
  12. 2018Model Reduction with Memory and the Machine Learning of Dynamical Systemscited by 19
7 more
  1. 2020MomentumRNN: Integrating Momentum into Recurrent Neural Networkscited by 18
  2. 2021How Does Momentum Benefit Deep Neural Networks Architecture Design? A Few Case Studiescited by 10
  3. 2018Reduced order modeling of subsurface multiphase flow models using deep residual recurrent neural networkscited by 9
  4. 2020Stochastic Gradient Descent with Nonlinear Conjugate Gradient-Style Adaptive Momentumcited by 8
  5. 2021Training Deep Neural Networks with Adaptive Momentum Inspired by the Quadratic Optimizationcited by 8
  6. 2021Neural Ordinary Differential Equations for Data-Driven Reduced Order Modeling of Environmental Hydrodynamicscited by 5
  7. 2021Data-driven reduced order modeling of environmental hydrodynamics using deep autoencoders and neural ODEscited by 2

Built on by

Cited by year

Citing papers per year: 2025: 2.

2 papers.

  1. 2025Variational Rank Reduction Autoencoders for Generative Thermal Designcited by 1
  2. 2025Application of Reduced-Order Models for Temporal Multiscale Representations in the Prediction of Dynamical Systemscited by 1