mlsanityData to 7 Oct 2026

Neural Ordinary Differential Equations for Nonlinear System Identification

arXiv 2203.00120 ↗First posted 28 Feb 2022cs.LG cs.SY eess.SYcited by 14

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Abstract (arXiv)

Neural ordinary differential equations (NODE) have been recently proposed as a promising approach for nonlinear system identification tasks. In this work, we systematically compare their predictive performance with current state-of-the-art nonlinear and classical linear methods. In particular, we present a quantitative study comparing NODE's performance against neural state-space models and classical linear system identification methods. We evaluate the inference speed and prediction performance of each method on open-loop errors across eight different dynamical systems. The experiments show that NODEs can consistently improve the prediction accuracy by an order of magnitude compared to benchmark methods. Besides improved accuracy, we also observed that NODEs are less sensitive to hyperparameters compared to neural state-space models. On the other hand, these performance gains come with a slight increase of computation at the inference time.

Key facts. Cited by 14 papers in the map (data through 7 Oct 2026). Builds on 27 of its 47 references that are in the map. First posted on arXiv 28 Feb 2022.

Builds on

27 of 47 references.

References · 27

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15 more
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 2; 2023: 1; 2024: 4; 2025: 2; 2026: 5.

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  1. 2023Deep networks for system identification: a Surveycited by 35
  2. 2022Operator inference with roll outs for learning reduced models from scarce and low-quality datacited by 11
  3. 2024Balanced Neural ODEs: nonlinear model order reduction and Koopman operator approximationscited by 3
  4. 2025Introducing Interval Neural Networks for Uncertainty-Aware System Identificationcited by 3
  5. 2026Understanding the Theoretical Foundations of Deep Neural Networks through Differential Equationscited by 1
  6. 2022Learning Time Delay Systems with Neural Ordinary Differential Equationscited by 0
  7. 2024SINDy vs Hard Nonlinearities and Hidden Dynamics: a Benchmarking Studycited by 0
  8. 2024Machine-Learned Closure of URANS for Stably Stratified Turbulence: Connecting Physical Timescales & Data Hyperparameters of Deep Time-Series Modelscited by 0
  9. 2024Lyapunov Neural ODE State-Feedback Control Policiescited by 0
  10. 2025Zero-Shot Function Encoder-Based Differentiable Predictive Controlcited by 0
  11. 2026xFODE+: Explainable Type-2 Fuzzy Additive ODEs for Uncertainty Quantificationcited by 0
  12. 2026xFODE: An Explainable Fuzzy Additive ODE Framework for System Identificationcited by 0
2 more
  1. 2026Beyond Prediction: Interval Neural Networks for Uncertainty-Aware System Identificationcited by 0
  2. 2026Learning partially observed systems with neural Hamiltonian ordinary differential equationscited by 0

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  7. 2024Deep Learning-based Approaches for State Space Models: A Selective Review
  8. 2025Structured Kolmogorov-Arnold Neural ODEs for Interpretable Learning and Symbolic Discovery of Nonlinear Dynamics