mlsanityData to 14 Oct 2026

Stable Neural Flows

arXiv 2003.08063 ↗First posted 18 Mar 2020cs.LG math.OC stat.MLcited by 25

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Abstract (arXiv)

We introduce a provably stable variant of neural ordinary differential equations (neural ODEs) whose trajectories evolve on an energy functional parametrised by a neural network. Stable neural flows provide an implicit guarantee on asymptotic stability of the depth-flows, leading to robustness against input perturbations and low computational burden for the numerical solver. The learning procedure is cast as an optimal control problem, and an approximate solution is proposed based on adjoint sensivity analysis. We further introduce novel regularizers designed to ease the optimization process and speed up convergence. The proposed model class is evaluated on non-linear classification and function approximation tasks.

Key facts. Cited by 25 papers in the map (data through 14 Oct 2026). First posted on arXiv 18 Mar 2020.

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 5; 2022: 3; 2023: 3; 2024: 5; 2025: 7; 2026: 2.

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  1. 2021Closed-form Continuous-time Neural Modelscited by 65
  2. 2021Constructing Neural Network-Based Models for Simulating Dynamical Systemscited by 31
  3. 2025Comprehensive Review of Neural Differential Equations for Time Series Analysiscited by 20
  4. 2022Robust Classification using Contractive Hamiltonian Neural ODEscited by 13
  5. 2025Stable Port-Hamiltonian Neural Networkscited by 13
  6. 2023Lyapunov-Stable Deep Equilibrium Modelscited by 10
  7. 2021Accelerating Neural ODEs Using Model Order Reductioncited by 9
  8. 2022Recognition Models to Learn Dynamics from Partial Observations with Neural ODEscited by 8
  9. 2023Unconstrained Parametrization of Dissipative and Contracting Neural Ordinary Differential Equationscited by 8
  10. 2024DeNOTS: Stable Deep Neural ODEs for Time Seriescited by 5
  11. 2024ControlSynth Neural ODEs: Modeling Dynamical Systems with Guaranteed Convergencecited by 5
  12. 2024Training Stiff Neural Ordinary Differential Equations with Explicit Exponential Integration Methodscited by 5
13 more
  1. 2021Optimal Energy Shaping via Neural Approximatorscited by 4
  2. 2024DualDynamics: Synergizing Implicit and Explicit Methods for Robust Irregular Time Series Analysiscited by 4
  3. 2021Learning Stochastic Optimal Policies via Gradient Descentcited by 3
  4. 2025The Vanishing Gradient Problem for Stiff Neural Differential Equationscited by 3
  5. 2025Deep Neural Networks Inspired by Differential Equationscited by 2
  6. 2024ICODE: Modeling Dynamical Systems with Extrinsic Input Informationcited by 1
  7. 2026Hybrid Energy-Based Models for Physical AI: Provably Stable Identification of Port-Hamiltonian Dynamicscited by 1
  8. 2022Modeling Nonlinear Dynamics in Continuous Time with Inductive Biases on Decay Rates and/or Frequenciescited by 0
  9. 2023Digital Twins for Patient Care via Knowledge Graphs and Closed-Form Continuous-Time Liquid Neural Networkscited by 0
  10. 2025Wavelet-Enhanced Neural ODE and Graph Attention for Interpretable Energy Forecastingcited by 0
  11. 2025Robust Convolution Neural ODEs via Contractivity-promoting regularizationcited by 0
  12. 2025Fine-Tuning Flow Matching via Maximum Likelihood Estimation of Reconstructionscited by 0
  13. 2026Markovian ODE-guided scoring can assess the quality of offline reasoning traces in language modelscited by 0