# Physics-based Reduced Order Modeling for Uncertainty Quantification of Guided Wave Propagation using Bayesian Optimization

arXiv: https://arxiv.org/abs/2307.09661 · HTML: https://mlsanity.com/paper/2307.09661/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 116 references that are in the map.
- First posted on arXiv 18 Jul 2023.

## Builds on (most cited first, 22 of 22)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [A Tutorial on Bayesian Optimization](https://mlsanity.com/paper/1807.02811/) (2018)
- [Hands-on Bayesian Neural Networks -- a Tutorial for Deep Learning Users](https://mlsanity.com/paper/2007.06823/) (2020)
- [Techniques for Interpretable Machine Learning](https://mlsanity.com/paper/1808.00033/) (2018)
- [Maximizing acquisition functions for Bayesian optimization](https://mlsanity.com/paper/1805.10196/) (2018)
- [Digital Twin: Values, Challenges and Enablers](https://mlsanity.com/paper/1910.01719/) (2019)
- [A Comprehensive Review of Digital Twin -- Part 1: Modeling and Twinning Enabling Technologies](https://mlsanity.com/paper/2208.14197/) (2022)
- [Digital twin, physics-based model, and machine learning applied to damage detection in structures](https://mlsanity.com/paper/2005.14360/) (2020)
- [Machine Learning Approach to Model Order Reduction of Nonlinear Systems via Autoencoder and LSTM Networks](https://mlsanity.com/paper/2109.11213/) (2021)
- [Maximum Likelihood Estimation in Gaussian Process Regression is Ill-Posed](https://mlsanity.com/paper/2203.09179/) (2022)
- [A greedy non-intrusive reduced order model for shallow water equations](https://mlsanity.com/paper/2002.11329/) (2020)
- [Recurrent Neural Networks and Long Short-Term Memory Networks: Tutorial and Survey](https://mlsanity.com/paper/2304.11461/) (2023)
- [Physics-informed machine learning for Structural Health Monitoring](https://mlsanity.com/paper/2206.15303/) (2022)
- [Online structural health monitoring by model order reduction and deep learning algorithms](https://mlsanity.com/paper/2103.14328/) (2021)
- [Uncertainty quantification of a three-dimensional in-stent restenosis model with surrogate modelling](https://mlsanity.com/paper/2111.06173/) (2021)
- [On a New Improvement-Based Acquisition Function for Bayesian Optimization](https://mlsanity.com/paper/1808.06918/) (2018)
- [textitFastSVD-ML-ROM: A Reduced-Order Modeling Framework based on Machine Learning for Real-Time Applications](https://mlsanity.com/paper/2207.11842/) (2022)
- [Inverse characterization of composites using guided waves and convolutional neural networks with dual-branch feature fusion](https://mlsanity.com/paper/2204.10486/) (2022)
- [Bayesian system identification for structures considering spatial and temporal correlation](https://mlsanity.com/paper/2305.00867/) (2023)
- [Physics-Informed Bayesian Learning of Electrohydrodynamic Polymer Jet Printing Dynamics](https://mlsanity.com/paper/2204.09513/) (2022)
- [Damage Identification in Fiber Metal Laminates using Bayesian Analysis with Model Order Reduction](https://mlsanity.com/paper/2206.04329/) (2022)

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

- [ShipNet: A Geometric Deep Learning Surrogate for Real-Time Ship Hydrodynamics](https://mlsanity.com/paper/2606.15356/) (2026)

## Abstract (arXiv)

In the context of digital twins, structural health monitoring (SHM) constitutes the backbone of condition-based maintenance, facilitating the interconnection between virtual and physical assets. Guided wave propagation (GWP) is commonly employed for the inspection of structures in SHM. However, GWP is sensitive to variations in the material properties of the structure, leading to false alarms. In this direction, uncertainty quantification (UQ) is regularly applied to improve the reliability of predictions. Computational mechanics is a useful tool for the simulation of GWP, and is often applied for UQ. Even so, the application of UQ methods requires numerous simulations, while large-scale, transient numerical GWP solutions increase the computational cost. Reduced order models (ROMs) are commonly employed to provide numerical results in a limited amount of time. In this paper, we propose a machine learning (ML)-based ROM, mentioned as BO-ML-ROM, to decrease the computational time related to the simulation of the GWP. The ROM is integrated with a Bayesian optimization (BO) framework, to adaptively sample the parameters for the ROM training. The finite element method is used for the simulation of the high-fidelity models. The formulated ROM is used for forward UQ of the GWP in an aluminum plate with varying material properties. To determine the influence of each parameter perturbation, a global, variance-based sensitivity analysis is implemented based on Sobol' indices. It is shown that Bayesian optimization outperforms one-shot sampling methods, both in terms of accuracy and speed-up. The predicted results reveal the efficiency of BO-ML-ROM for GWP and demonstrate its value for UQ.