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

• We introduce mNARX + , a novel data-driven surrogate model for complex dynamical systems. • mNARX + combines manifold-NARX (mNARX) with the feature-based structure of functional-NARX ( F -NARX). • It also automates the construction of mNARX models, strongly reducing its reliance on domain expertise. • A recursive, data-driven algorithm automatically identifies key auxiliary quantities and their modeling sequence. • It provides a systematic and automated path to creating accurate surrogates for challenging dynamical problems. 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.