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

arXiv: https://arxiv.org/abs/2507.13301 · HTML: https://mlsanity.com/paper/2507.13301/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 52 references that are in the map.
- First posted on arXiv 17 Jul 2025.

## Builds on (most cited first, 3 of 3)

- [Assessment of DeepONet for reliability analysis of stochastic nonlinear dynamical systems](https://mlsanity.com/paper/2201.13145/) (2022)
- [Surrogate modeling with functional nonlinear autoregressive models (F-NARX)](https://mlsanity.com/paper/2410.07293/) (2024)
- [Emulating the dynamics of complex systems using autoregressive models on manifolds (mNARX)](https://mlsanity.com/paper/2306.16335/) (2023)

## Built on by (most cited first, 2 of 2)

- [High-dimensional reliability-based design optimization using stochastic emulators](https://mlsanity.com/paper/2604.05759/) (2026)
- [Probabilistic function-on-function nonlinear autoregressive model for emulation and reliability analysis of stochastic dynamical systems](https://mlsanity.com/paper/2602.01929/) (2026)

## Abstract (arXiv)

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.