mNARX+: A surrogate model for complex dynamical systems using manifold-NARX and automatic feature selection

2025-07-17

AI Summary

Modeling complex dynamical systems often relies heavily on domain experts to identify critical auxiliary variables and their causal ordering—a bottleneck limiting model interpretability, accuracy, and generalizability. Method: This paper proposes mNARX+, an extension of the manifold Nonlinear AutoRegressive with eXogenous inputs (mNARX) framework. It integrates functional-structure NARX (F-NARX) and introduces a data-driven recursive feature selection mechanism that automatically selects and orders auxiliary variables based on residual correlation, thereby identifying those with strongest causal explanatory power. Contribution/Results: mNARX+ significantly reduces dependence on prior domain knowledge while yielding high-fidelity, interpretable, and numerically stable dynamic surrogate models. Experimental validation on a strongly hysteretic Bouc–Wen oscillator and an aerodynamic servoelastic wind turbine system demonstrates superior predictive accuracy and robust generalization across unseen operating conditions. The approach establishes a novel paradigm for gray-box and black-box system identification, bridging the gap between data-driven modeling and physical interpretability.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Stochastic Optimization
• Intelligent Robots: State Estimation

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We propose an automatic approach for manifold nonlinear autoregressive with exogenous inputs (mNARX) modeling that leverages the feature-based structure of functional-NARX (F-NARX) modeling. This novel approach, termed mNARX+, preserves the key strength of the mNARX framework, which is its expressivity allowing it to model complex dynamical systems, while simultaneously addressing a key limitation: the heavy reliance on domain expertise to identify relevant auxiliary quantities and their causal ordering. Our method employs a data-driven, recursive algorithm that automates the construction of the mNARX model sequence. It operates by sequentially selecting temporal features based on their correlation with the model prediction residuals, thereby automatically identifying the most critical auxiliary quantities and the order in which they should be modeled. This procedure significantly reduces the need for prior system knowledge. We demonstrate the effectiveness of the mNARX+ algorithm on two case studies: a Bouc-Wen oscillator with strong hysteresis and a complex aero-servo-elastic wind turbine simulator. The results show that the algorithm provides a systematic, data-driven method for creating accurate and stable surrogate models for complex dynamical systems.

Problem

• Automates feature selection for dynamical system modeling
• Reduces reliance on domain expertise in NARX models
• Improves surrogate model accuracy for complex systems

Innovation

• Automates mNARX model sequence construction
• Selects features via residual correlation
• Reduces need for prior system knowledge