We present a new Subset Simulation approach using Hamiltonian neural network-based Monte Carlo sampling for reliability analysis. The proposed strategy combines the superior sampling of the Hamiltonian Monte Carlo method with computationally efficient gradient evaluations using Hamiltonian neural networks. This combination is especially advantageous because the neural network architecture conserves the Hamiltonian, which defines the acceptance criteria of the Hamiltonian Monte Carlo sampler. Hence, this strategy achieves high acceptance rates at low computational cost. Our approach estimates small failure probabilities using Subset Simulations. However, in low-probability sample regions, the gradient evaluation is particularly challenging. The remarkable accuracy of the proposed strategy is demonstrated on different reliability problems, and its efficiency is compared to the traditional Hamiltonian Monte Carlo method. We note that this approach can reach its limitations for gradient estimations in low-probability regions of complex and high-dimensional distributions. Thus, we propose techniques to improve gradient prediction in these particular situations and enable accurate estimations of the probability of failure. The highlight of this study is the reliability analysis of a system whose parameter distributions must be inferred with Bayesian inference problems. In such a case, the Hamiltonian Monte Carlo method requires a full model evaluation for each gradient evaluation and, therefore, comes at a very high cost. However, using Hamiltonian neural networks in this framework replaces the expensive model evaluation, resulting in tremendous improvements in computational efficiency.

翻译：我们提出一种基于哈密顿神经网络蒙特卡洛采样的新型子集模拟方法，用于可靠性分析。该策略将哈密顿蒙特卡洛方法的优越采样能力与利用哈密顿神经网络进行高效梯度评估相结合。这种组合具有显著优势，因为神经网络结构能够守恒定义哈密顿蒙特卡洛采样器接受准则的哈密顿量，从而以较低计算成本实现高接受率。该方法通过子集模拟估计小失效概率，但在低概率样本区域中梯度评估尤为困难。所提策略的卓越精度通过不同可靠性问题得到验证，其效率与传统哈密顿蒙特卡洛方法进行对比。我们注意到，该方法在处理复杂高维分布的低概率区域梯度估计时可能达到性能极限。为此，我们提出改进这些特定情况下梯度预测的技术，以实现失效概率的精确估计。本研究的亮点在于解决必须通过贝叶斯推断裂断参数分布的系统可靠性问题。在此类场景中，哈密顿蒙特卡洛方法每次梯度评估均需完整模型计算，导致极高性能开销。而采用哈密顿神经网络框架可替代昂贵的模型评估，从而实现计算效率的极大提升。