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

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.

Surrogate modeling for uncertainty quantification in nonlinear dynamics

Predicting the behavior of complex systems in engineering often involves significant uncertainty about operating conditions, such as external loads, environmental effects, and manufacturing variability. As a result, uncertainty quantification (UQ) has become a critical tool in modeling-based engineering, providing methods to identify, characterize, and propagate uncertainty through computational models. However, the stochastic nature of UQ typically requires numerous evaluations of these models, which can be computationally expensive and limit the scope of feasible analyses. To address this, surrogate models, i.e., efficient functional approximations trained on a limited set of simulations, have become central in modern UQ practice. This book chapter presents a concise review of surrogate modeling techniques for UQ, with a focus on the particularly challenging task of capturing the full time-dependent response of dynamical systems. It introduces a classification of time-dependent problems based on the complexity of input excitation and discusses corresponding surrogate approaches, including combinations of principal component analysis with polynomial chaos expansions, time warping techniques, and nonlinear autoregressive models with exogenous inputs (NARX models). Each method is illustrated with simple application examples to clarify the underlying ideas and practical use.