Deep Learning-Based Multi-Fidelity Surrogate Modeling for High Dimensional Reliability Prediction

Abstract Multifidelity surrogate modeling offers a cost-effective approach to reducing extensive evaluations of expensive physics-based simulations for reliability prediction. However, considering spatial uncertainties in multifidelity surrogate modeling remains extremely challenging due to the curse of dimensionality. To address this challenge, this paper introduces a deep learning-based multifidelity surrogate modeling approach that fuses multifidelity datasets for high-dimensional reliability analysis of complex structures. It first involves a heterogeneous dimension transformation approach to bridge the gap in terms of input format between the low-fidelity and high-fidelity domains. Then, an explainable deep convolutional dimension-reduction network (ConvDR) is proposed to effectively reduce the dimensionality of the structural reliability problems. To obtain a meaningful low-dimensional space, a new knowledge reasoning-based loss regularization mechanism is integrated with the covariance matrix adaptation evolution strategy (CMA-ES) to encourage an unbiased linear pattern in the latent space for reliability prediction. Then, the high-fidelity data can be utilized for bias modeling using Gaussian process (GP) regression. Finally, Monte Carlo simulation (MCS) is employed for the propagation of high-dimensional spatial uncertainties. Two structural examples are utilized to validate the effectiveness of the proposed method.