TY - JOUR

T1 - Novel gradient-enhanced Bayesian neural networks for uncertainty propagation

AU - Shi, Yan

AU - Chai, Rui

AU - Beer, Michael

N1 - Publisher Copyright: © 2024 The Author(s)

PY - 2024/9/1

Y1 - 2024/9/1

N2 - Uncertainty propagation (UP) is crucial for assessing the impact of input uncertainty on structural responses, holding significant importance in engineering applications. However, achieving accurate and efficient UP remains challenging, especially for highly nonlinear structures. Bayesian neural networks (BNN) have gained attention for addressing UP issues, yet current BNN models only utilize input samples and corresponding structural responses for training. However, incorporating gradients of structural responses with respect to input samples provides valuable information. This study proposes a novel approach called gradient-enhanced Bayesian neural networks (GEBNN) to tackle UP tasks. In the GEBNN, a modified evidence lower bound (MELBO) loss is developed to consider both structural responses and gradient information simultaneously. This includes disparities between actual and predicted responses, as well as disparities between actual and predicted derivatives. Additionally, a gradient screening strategy based on the marginal probability density functions (PDFs) of input samples is established to identify significant derivative data for GEBNN training. Once the GEBNN is configured, it is utilized to replace the computationally intensive finite element model to efficiently provide UP results. Various applications, including nonlinear numerical examples, and mechanical, civil, and aeronautical structures, are presented to demonstrate the effectiveness of the GEBNN. The results show that the GEBNN significantly enhances the computational accuracy of the BNN in solving UP tasks.

AB - Uncertainty propagation (UP) is crucial for assessing the impact of input uncertainty on structural responses, holding significant importance in engineering applications. However, achieving accurate and efficient UP remains challenging, especially for highly nonlinear structures. Bayesian neural networks (BNN) have gained attention for addressing UP issues, yet current BNN models only utilize input samples and corresponding structural responses for training. However, incorporating gradients of structural responses with respect to input samples provides valuable information. This study proposes a novel approach called gradient-enhanced Bayesian neural networks (GEBNN) to tackle UP tasks. In the GEBNN, a modified evidence lower bound (MELBO) loss is developed to consider both structural responses and gradient information simultaneously. This includes disparities between actual and predicted responses, as well as disparities between actual and predicted derivatives. Additionally, a gradient screening strategy based on the marginal probability density functions (PDFs) of input samples is established to identify significant derivative data for GEBNN training. Once the GEBNN is configured, it is utilized to replace the computationally intensive finite element model to efficiently provide UP results. Various applications, including nonlinear numerical examples, and mechanical, civil, and aeronautical structures, are presented to demonstrate the effectiveness of the GEBNN. The results show that the GEBNN significantly enhances the computational accuracy of the BNN in solving UP tasks.

KW - Bayesian neural networks

KW - Evidence lower bound loss

KW - Gradient information

KW - Gradient screening strategy

KW - Uncertainty propagation

UR - http://www.scopus.com/inward/record.url?scp=85197352472&partnerID=8YFLogxK

U2 - 10.1016/j.cma.2024.117188

DO - 10.1016/j.cma.2024.117188

M3 - Article

AN - SCOPUS:85197352472

VL - 429

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

SN - 0045-7825

M1 - 117188

ER -