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

2026-01-24

AI Summary

This work addresses the suboptimality arising from the decoupling of model structure selection and parameter learning in nonlinear dynamic system modeling. To overcome this limitation, the authors propose a novel method that jointly optimizes model class selection and parameter estimation within a set-membership framework, specifically tailored for the NARX-ESN (Nonlinear Autoregressive with Exogenous inputs–Echo State Network) model family incorporating autoregressive terms. The approach uniquely integrates simulation consistency evaluation into the set-membership learning process, thereby circumventing the NP-hard optimization challenges inherent in autoregressive models. Experimental results demonstrate that the proposed algorithm identifies dynamic models that are structurally parsimonious, highly accurate, and robust under bounded noise conditions, significantly enhancing both generalization performance and suitability for control applications.

Technology Category

• Natural Language Processing: Learning & Optimization for NLP
• Machine Learning: Structured Learning
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• model class selection
• parameter learning
• nonlinear dynamical systems
• NARX ESNs
• robust training

Innovation

• set-membership
• NARX-ESN
• joint model selection
• robust training
• nonlinear dynamical systems identification