Structural reliability evaluation for composites constitutes a fundamentally high-dimensional multiscale problem, as microscale material uncertainties must propagate to the macroscale and can be quantified as high-dimensional random fields. Conventional approaches are computationally intractable, as they rely on repeatedly solving coupled partial differential equation systems across scales while contending with the exponential complexity inherent in high-dimensional uncertainty quantification. This work introduces a scalable and physically consistent framework that addresses both bottlenecks simultaneously in the case of separation of scales and (anisotropic) linear elasticity. In particular, we couple a physics-augmented Voigt--Reuss Neural Network (VRNN) with the Deep Inverse Rosenblatt Transport (DIRT) method to estimate the posterior probability of structural failure. The VRNN is used to resolve the computationally expensive FE$^2$ scheme by providing a near-instantaneous evaluation of the homogenized stiffness tensor that is guaranteed to be symmetric, positive-definite, and strictly bounded within the Voigt--Reuss limits, enabling fast evaluation of the homogenized responses. The DIRT method constructs a sequence of functional tensor train approximations to efficiently store an approximation of the high-dimensional optimal importance sampling distribution for estimating the probability of failure. This mitigates the curse of dimensionality arising from the Karhunen--Loève expansion of the random fields. The framework is demonstrated on a three-dimensional heterogeneous benchmark problem, where the uncertainty in the microscale material properties is characterized by a Bayesian posterior distribution obtained from limited strain observations. Our results show that the proposed framework can provide low-variance estimates of failure probabilities in dimensions up to 150.

翻译：复合材料的结构可靠性评估本质上是一个高维多尺度问题，因为微观尺度的材料不确定性必须传播至宏观尺度，并可量化为高维随机场。传统方法在计算上难以处理，因为它们需要反复求解跨尺度的耦合偏微分方程组，同时还要应对高维不确定性量化固有的指数级复杂度。本文提出了一种可扩展且物理一致的框架，在尺度分离与（各向异性）线弹性条件下同步解决了这两个瓶颈。具体而言，我们将物理增强的Voigt-Reuss神经网络（VRNN）与深度逆Rosenblatt变换（DIRT）方法相结合，以估计结构失效的后验概率。VRNN通过提供同化刚度张量的近瞬态评估来解决计算代价高昂的FE²方案，该张量被保证具有对称性、正定性和严格受限于Voigt-Reuss界限的特性，从而实现了同化响应的快速评估。DIRT方法构建了一序列函数式张量列近似，以高效存储高维最优重要性采样分布的近似，用于估计失效概率。这缓解了由随机场的Karhunen-Loève展开引发的维度灾难。该框架在一个三维异质性基准问题上进行了验证，其中微观尺度材料特性的不确定性由从有限应变观测中获得的贝叶斯后验分布表征。我们的结果表明，所提出的框架能在高达150维的空间中提供低方差的失效概率估计。