# Surrogate modeling for uncertainty quantification in nonlinear dynamics

arXiv: https://arxiv.org/abs/2507.12358 · HTML: https://mlsanity.com/paper/2507.12358/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 64 references that are in the map.
- First posted on arXiv 16 Jul 2025.

## Builds on (most cited first, 7 of 7)

- [Sparse Polynomial Chaos Expansions: Literature Survey and Benchmark](https://mlsanity.com/paper/2002.01290/) (2020)
- [Automatic selection of basis-adaptive sparse polynomial chaos expansions for engineering applications](https://mlsanity.com/paper/2009.04800/) (2020)
- [Assessment of DeepONet for reliability analysis of stochastic nonlinear dynamical systems](https://mlsanity.com/paper/2201.13145/) (2022)
- [A least-squares method for sparse low rank approximation of multivariate functions](https://mlsanity.com/paper/1305.0030/) (2013)
- [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)
- [Bayesian full waveform inversion with sequential surrogate model refinement](https://mlsanity.com/paper/2505.03246/) (2025)

## Built on by (most cited first, 1 of 1)

- [Uncertainty propagation in auto-regressive random neural network models](https://mlsanity.com/paper/2608.20483/) (2026)

## Abstract (arXiv)

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.