Reliability Analysis of Complex Systems using Subset Simulations with
  Hamiltonian Neural Networks
Denny Thaler Somayajulu L. N. Dhulipala Franz Bamer Bernd Markert Michael D. Shields
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.