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

TL;DR

The paper introduces mNARX+, an automated, data-driven surrogate modeling approach for complex dynamical systems that reduces reliance on domain expertise through recursive feature selection.

Contribution

It presents a novel automatic method for constructing mNARX models using correlation-based feature selection, enhancing expressivity and reducing expert knowledge requirements.

Findings

Successfully modeled a Bouc-Wen oscillator with hysteresis.

Accurately simulated a complex wind turbine system.

Automated feature selection improved model stability.

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.