TY - JOUR

T1 - Physics-guided mixture density networks for uncertainty quantification

AU - Chen, Jie

AU - Yu, Yang

AU - Liu, Yongming

N1 - Funding Information:
The research reported in this paper was supported partially by funds from the NASA University Leadership Initiative program (Contract No. NNX17AJ86A , Project Officer: Dr. Anupa Bajwa, Principal Investigator: Dr. Yongming Liu). The support is gratefully acknowledged.
Publisher Copyright:
© 2022 Elsevier Ltd

PY - 2022/12

Y1 - 2022/12

N2 - This paper proposes a Physics-guided Mixture Density Network (PgMDN) model for uncertainty quantification of regression-type analysis. It integrates a Mixture Density Network for probabilistic modeling and physics knowledge as regularizations. This model can handle arbitrary distribution of data (e.g., strongly non-Gaussian, multi-mode, and truncated distributions). The physics knowledge from parameters and their partial derivatives is used as equality/ inequality constraints. The training of physics-guided machine learning is formulated as a constrained optimization problem. The constrained optimization problem is transformed to an unconstrained one using a dynamic penalty function algorithm. Thus, the commonly used backpropagation algorithm can be used to train the neural network. With the physics constraints, the required training data size can be reduced, and the overfitting problem can be mitigated. This paper demonstrates the application of the PgMDN using a numerical example, an engineering problem for fatigue stress-life curve estimation, an engineering problem for natural frequency prediction of bridges, and an engineering problem for fatigue life prediction of corroded steel reinforcing bars. Some discussions are given to illustrate the effectiveness of incorporating the physics knowledge when data are sparse, the improvement of the dynamic penalty function method compared with the static method, and the benefits achieved from the distribution mixture compared with a single Gaussian distribution.

AB - This paper proposes a Physics-guided Mixture Density Network (PgMDN) model for uncertainty quantification of regression-type analysis. It integrates a Mixture Density Network for probabilistic modeling and physics knowledge as regularizations. This model can handle arbitrary distribution of data (e.g., strongly non-Gaussian, multi-mode, and truncated distributions). The physics knowledge from parameters and their partial derivatives is used as equality/ inequality constraints. The training of physics-guided machine learning is formulated as a constrained optimization problem. The constrained optimization problem is transformed to an unconstrained one using a dynamic penalty function algorithm. Thus, the commonly used backpropagation algorithm can be used to train the neural network. With the physics constraints, the required training data size can be reduced, and the overfitting problem can be mitigated. This paper demonstrates the application of the PgMDN using a numerical example, an engineering problem for fatigue stress-life curve estimation, an engineering problem for natural frequency prediction of bridges, and an engineering problem for fatigue life prediction of corroded steel reinforcing bars. Some discussions are given to illustrate the effectiveness of incorporating the physics knowledge when data are sparse, the improvement of the dynamic penalty function method compared with the static method, and the benefits achieved from the distribution mixture compared with a single Gaussian distribution.

KW - Constrained optimization

KW - Neural network

KW - Physics-guided machine learning

KW - Probabilistic

KW - Uncertainty quantification

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U2 - 10.1016/j.ress.2022.108823

DO - 10.1016/j.ress.2022.108823

M3 - Article

AN - SCOPUS:85138068758

VL - 228

JO - Reliability Engineering and System Safety

JF - Reliability Engineering and System Safety

SN - 0951-8320

M1 - 108823

ER -