Abstract
A Physics-guided Mixture Density Network (PgMDN) model is proposed for uncertainty quantification of fatigue data analysis in this paper. 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 the physics-guided machine learning is formulated as a constrained optimization problem. To train the neural network with the commonly used backpropagation algorithm, the constrained optimization problem is transformed to an unconstrained one using a dynamic penalty function algorithm. With the physics constraints, the required training data sized can be reduced and the overfitting problem can be mitigated. The PgMDN is applied for fatigue stress-life curve estimation for multiple data sets. Some discussions are given to illustrate the effectiveness of incorporating the physics knowledge, 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.
