# Model structures and fitting criteria for system identification with neural networks

arXiv: https://arxiv.org/abs/1911.13034 · HTML: https://mlsanity.com/paper/1911.13034/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Nov 2019.

## Built on by (most cited first, 16 of 16)

- [On Recurrent Neural Networks for learning-based control: recent results and ideas for future developments](https://mlsanity.com/paper/2111.13557/) (2021)
- [Meta-Learning of Neural State-Space Models Using Data From Similar Systems](https://mlsanity.com/paper/2211.07768/) (2022)
- [Nonlinear MPC for Offset-Free Tracking of systems learned by GRU Neural Networks](https://mlsanity.com/paper/2103.02383/) (2021)
- [Improved Initialization of State-Space Artificial Neural Networks](https://mlsanity.com/paper/2103.14516/) (2021)
- [Recurrent Neural Network Training with Convex Loss and Regularization Functions by Extended Kalman Filtering](https://mlsanity.com/paper/2111.02673/) (2021)
- [Learning neural state-space models: do we need a state estimator?](https://mlsanity.com/paper/2206.12928/) (2022)
- [Meta-Learning for Physically-Constrained Neural System Identification](https://mlsanity.com/paper/2501.06167/) (2025)
- [Recurrent Neural Network-based Internal Model Control design for stable nonlinear systems](https://mlsanity.com/paper/2108.04585/) (2021)
- [AI-Aided Kalman Filters](https://mlsanity.com/paper/2410.12289/) (2024)
- [dynoGP: Deep Gaussian Processes for dynamic system identification](https://mlsanity.com/paper/2502.05620/) (2025)
- [Deep learning with transfer functions: new applications in system identification](https://mlsanity.com/paper/2104.09839/) (2021)
- [Neural State-Space Models: Empirical Evaluation of Uncertainty Quantification](https://mlsanity.com/paper/2304.06349/) (2023)
- [Identification For Control Based on Neural Networks: Approximately Linearizable Models](https://mlsanity.com/paper/2409.15858/) (2024)
- [Autoregressive models for biomedical signal processing](https://mlsanity.com/paper/2304.11070/) (2023)
- [A neural network-based approach to hybrid systems identification for control](https://mlsanity.com/paper/2404.01814/) (2024)
- [Space-Filling Regularization for Robust and Interpretable Nonlinear State Space Models](https://mlsanity.com/paper/2507.07792/) (2025)

## Abstract (arXiv)

This paper focuses on the identification of dynamical systems with tailor-made model structures, where neural networks are used to approximate uncertain components and domain knowledge is retained, if available. These model structures are fitted to measured data using different criteria including a computationally efficient approach minimizing a regularized multi-step ahead simulation error. In this approach, the neural network parameters are estimated along with the initial conditions used to simulate the output signal in small-size subsequences. A regularization term is included in the fitting cost in order to enforce these initial conditions to be consistent with the estimated system dynamics. Pitfalls and limitations of naive one-step prediction and simulation error minimization are also discussed.