# Nonlinear Systems Identification Using Deep Dynamic Neural Networks

arXiv: https://arxiv.org/abs/1610.01439 · HTML: https://mlsanity.com/paper/1610.01439/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Oct 2016.

## Built on by (most cited first, 14 of 14)

- [Constructing Neural Network-Based Models for Simulating Dynamical Systems](https://mlsanity.com/paper/2111.01495/) (2021)
- [Physics-Informed Machine Learning for Modeling and Control of Dynamical Systems](https://mlsanity.com/paper/2306.13867/) (2023)
- [Neural Ordinary Differential Equations for Nonlinear System Identification](https://mlsanity.com/paper/2203.00120/) (2022)
- [Gradient-Based Trajectory Optimization With Learned Dynamics](https://mlsanity.com/paper/2204.04558/) (2022)
- [Recurrent Neural Network-based Internal Model Control design for stable nonlinear systems](https://mlsanity.com/paper/2108.04585/) (2021)
- [Bounded nonlinear forecasts of partially observed geophysical systems with physics-constrained deep learning](https://mlsanity.com/paper/2202.05750/) (2022)
- [A Neural Network Ensemble Approach to System Identification](https://mlsanity.com/paper/2110.08382/) (2021)
- [Safety Filter Design for Neural Network Systems via Convex Optimization](https://mlsanity.com/paper/2308.08086/) (2023)
- [Data-driven identification of nonlinear dynamical systems with LSTM autoencoders and Normalizing Flows](https://mlsanity.com/paper/2503.03977/) (2025)
- [Dynamical System Parameter Identification using Deep Recurrent Cell Networks](https://mlsanity.com/paper/2107.02427/) (2021)
- [Assured Neural Network Architectures for Control and Identification of Nonlinear Systems](https://mlsanity.com/paper/2109.10298/) (2021)
- [Symbolic Learning of Interpretable Reduced-Order Models for Jumping Quadruped Robots](https://mlsanity.com/paper/2508.06538/) (2025)
- [Deep learning-based pavement performance modeling using multiple distress indicators and road work history](https://mlsanity.com/paper/2605.01914/) (2026)
- [Frequency-Domain Neural ODEs for Modeling Non-Linear Dynamical Systems](https://mlsanity.com/paper/2606.22075/) (2026)

## Abstract (arXiv)

Neural networks are known to be effective function approximators. Recently, deep neural networks have proven to be very effective in pattern recognition, classification tasks and human-level control to model highly nonlinear realworld systems. This paper investigates the effectiveness of deep neural networks in the modeling of dynamical systems with complex behavior. Three deep neural network structures are trained on sequential data, and we investigate the effectiveness of these networks in modeling associated characteristics of the underlying dynamical systems. We carry out similar evaluations on select publicly available system identification datasets. We demonstrate that deep neural networks are effective model estimators from input-output data