Consistency regularization-based deep polynomial chaos neural network method for reliability analysis

Polynomial chaos expansion (PCE) is a powerful method for building a surrogate model that can be applied to assist reliability analysis. Generally, a PCE model with a higher expansion order is required to obtain an accurate surrogate model for some complex non-linear stochastic systems. However, the high-order PCE increases the number of labeled data necessary for solving the expansion coefficients. To alleviate this problem, this paper proposes a consistency regularization-based deep polynomial chaos neural network (Deep PCNN) method, including the low-order adaptive PCE model (the auxiliary model) and the high-order polynomial chaos neural network (the main model). The expansion coefficients of the main model are parameterized into the learnable weights of the polynomial chaos neural network, realizing iterative learning of expansion coefficients to obtain more accurate high-order PCE models. By unlabeled data, the auxiliary model uses the proposed consistency regularization loss function to assist in training the main model. The consistency regularization-based Deep PCNN method can precisely solve the expansion coefficients with fewer labeled data without reducing the high-order PCE model accuracy compared to the existing PCE methods. Two numerical examples validate the effectiveness of the consistency regularization-based Deep PCNN method, which is then applied to satellite reliability analysis.