Surrogate modeling for uncertainty quantification in nonlinear dynamics

2025-07-16

AI Summary

To address the high computational cost of predicting dynamic responses of nonlinear dynamical systems under multi-source uncertainties (e.g., external loads, environmental disturbances, manufacturing variations), this paper proposes an efficient time-varying uncertainty quantification (UQ) framework. The method introduces a novel time-dependent problem classification scheme based on input excitation complexity and integrates principal component analysis (PCA) for dimensionality reduction, polynomial chaos expansion (PCE) for uncertainty propagation, dynamic time warping (DTW) for temporal alignment of response trajectories, and NARX neural networks for sequence modeling—enabling high-fidelity surrogate approximation of full-time-history responses. The framework significantly improves UQ efficiency: across multiple benchmark cases, it reduces high-fidelity simulation calls by one to two orders of magnitude while preserving statistical convergence and fidelity to key dynamic features. This establishes a scalable, real-time-capable UQ paradigm for complex nonlinear systems.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Uncertainty Representations
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

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• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Abstract

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.

Problem

• Quantify uncertainty in nonlinear dynamics using surrogate models
• Reduce computational cost of uncertainty quantification in complex systems
• Capture time-dependent responses in dynamical systems efficiently

Innovation

• Surrogate models for efficient uncertainty quantification
• Principal component analysis with polynomial chaos
• Nonlinear autoregressive models with exogenous inputs