# Neural Ordinary Differential Equations for Nonlinear System Identification

arXiv: https://arxiv.org/abs/2203.00120 · HTML: https://mlsanity.com/paper/2203.00120/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 47 references that are in the map.
- First posted on arXiv 28 Feb 2022.

## Builds on (most cited first, 27 of 27)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Decoupled Weight Decay Regularization](https://mlsanity.com/paper/1711.05101/) (2017)
- [Learning Latent Dynamics for Planning from Pixels](https://mlsanity.com/paper/1811.04551/) (2018)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [Interaction Networks for Learning about Objects, Relations and Physics](https://mlsanity.com/paper/1612.00222/) (2016)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [Universal Differential Equations for Scientific Machine Learning](https://mlsanity.com/paper/2001.04385/) (2020)
- [Stable Architectures for Deep Neural Networks](https://mlsanity.com/paper/1705.03341/) (2017)
- [Symplectic ODE-Net: Learning Hamiltonian Dynamics with Control](https://mlsanity.com/paper/1909.12077/) (2019)
- [Structured Inference Networks for Nonlinear State Space Models](https://mlsanity.com/paper/1609.09869/) (2016)
- [Dissecting Neural ODEs](https://mlsanity.com/paper/2002.08071/) (2020)
- [Neural Jump Stochastic Differential Equations](https://mlsanity.com/paper/1905.10403/) (2019)
- [A Differentiable Programming System to Bridge Machine Learning and Scientific Computing](https://mlsanity.com/paper/1907.07587/) (2019)
- [DiffEqFlux.jl - A Julia Library for Neural Differential Equations](https://mlsanity.com/paper/1902.02376/) (2019)
- [SNODE: Spectral Discretization of Neural ODEs for System Identification](https://mlsanity.com/paper/1906.07038/) (2019)
- [DyNODE: Neural Ordinary Differential Equations for Dynamics Modeling in Continuous Control](https://mlsanity.com/paper/2009.04278/) (2020)
- [TorchDyn: A Neural Differential Equations Library](https://mlsanity.com/paper/2009.09346/) (2020)
- [Nonlinear Systems Identification Using Deep Dynamic Neural Networks](https://mlsanity.com/paper/1610.01439/) (2016)
- [Constrained Neural Ordinary Differential Equations with Stability Guarantees](https://mlsanity.com/paper/2004.10883/) (2020)
- [Learning Constrained Adaptive Differentiable Predictive Control Policies With Guarantees](https://mlsanity.com/paper/2004.11184/) (2020)
- [Physics-Informed Neural State Space Models via Learning and Evolution](https://mlsanity.com/paper/2011.13497/) (2020)
- [Constrained Block Nonlinear Neural Dynamical Models](https://mlsanity.com/paper/2101.01864/) (2021)
- [Accelerating Neural ODEs Using Model Order Reduction](https://mlsanity.com/paper/2105.14070/) (2021)
- [Predicting dynamical system evolution with residual neural networks](https://mlsanity.com/paper/1910.05233/) (2019)

## Built on by (most cited first, 15 of 15)

- [Deep networks for system identification: a Survey](https://mlsanity.com/paper/2301.12832/) (2023)
- [Operator inference with roll outs for learning reduced models from scarce and low-quality data](https://mlsanity.com/paper/2212.01418/) (2022)
- [Balanced Neural ODEs: nonlinear model order reduction and Koopman operator approximations](https://mlsanity.com/paper/2410.10174/) (2024)
- [Introducing Interval Neural Networks for Uncertainty-Aware System Identification](https://mlsanity.com/paper/2504.18845/) (2025)
- [Understanding the Theoretical Foundations of Deep Neural Networks through Differential Equations](https://mlsanity.com/paper/2603.18331/) (2026)
- [Learning Time Delay Systems with Neural Ordinary Differential Equations](https://mlsanity.com/paper/2206.14288/) (2022)
- [SINDy vs Hard Nonlinearities and Hidden Dynamics: a Benchmarking Study](https://mlsanity.com/paper/2403.00578/) (2024)
- [Machine-Learned Closure of URANS for Stably Stratified Turbulence: Connecting Physical Timescales & Data Hyperparameters of Deep Time-Series Models](https://mlsanity.com/paper/2404.16141/) (2024)
- [Lyapunov Neural ODE State-Feedback Control Policies](https://mlsanity.com/paper/2409.00393/) (2024)
- [Zero-Shot Function Encoder-Based Differentiable Predictive Control](https://mlsanity.com/paper/2511.05757/) (2025)
- [SSP: Safety-guaranteed Surgical Policy via Joint Optimization of Behavioral and Spatial Constraints](https://mlsanity.com/paper/2603.07032/) (2026)
- [xFODE+: Explainable Type-2 Fuzzy Additive ODEs for Uncertainty Quantification](https://mlsanity.com/paper/2604.14880/) (2026)
- [xFODE: An Explainable Fuzzy Additive ODE Framework for System Identification](https://mlsanity.com/paper/2604.14883/) (2026)
- [Beyond Prediction: Interval Neural Networks for Uncertainty-Aware System Identification](https://mlsanity.com/paper/2605.11460/) (2026)
- [Learning partially observed systems with neural Hamiltonian ordinary differential equations](https://mlsanity.com/paper/2605.23510/) (2026)

## 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.