A new approach for combined model class selection and parameters learning for auto-regressive neural models

TL;DR

This work tackles nonlinear dynamical system identification by jointly selecting a model class and learning its parameters within the NARXESN family. It introduces a set-membership framework that computes a Feasible Parameter Set (FPS) and uses a data-driven set-distance $d^*_{\mathcal{S}}$ to compare candidate models under bounded measurement noise $\bar{w}$. The method combines forward regressor selection via SDRR, iterative numerical hyperparameter tuning, and scenario-based evaluation to identify parsimonious yet accurate NARXESN models, demonstrated on simulated and real Wiener–Hammerstein data with high predictive fidelity ($\mathrm{FIT}$ up to $95.39\%$). The approach yields robust, data-consistent models suitable for control applications, with clear implications for handling noise and avoiding overfitting in nonlinear system identification. Future work points to extending the framework to broader model families and nonlinear controllers while maintaining computational efficiency.

Abstract

This work introduces a novel approach for the joint selection of model structure and parameter learning for nonlinear dynamical systems identification. Focusing on a specific Recurrent Neural Networks (RNNs) family, i.e., Nonlinear Auto-Regressive with eXogenous inputs Echo State Networks (NARXESNs), the method allows to simultaneously select the optimal model class and learn model parameters from data through a new set-membership (SM) based procedure. The results show the effectiveness of the approach in identifying parsimonious yet accurate models suitable for control applications. Moreover, the proposed framework enables a robust training strategy that explicitly accounts for bounded measurement noise and enhances model robustness by allowing data-consistent evaluation of simulation performance during parameter learning, a process generally NP-hard for models with autoregressive components.

Figures (7)

• Figure 1: Flow chart of Algorithm \ref{['alg:NARXESNmodelStructureSelection']}.
• Figure 2: MPRS input signal applied to the simulated NARXESN system.
• Figure 3: Simulation of the identified NARXESN model on the validation dataset.
• Figure 4: Block diagram of the Wiener–Hammerstein Benchmark system.
• Figure 5: Simulation of the selected NARXESN model on the validation dataset.